MAY 18: Deputy Defence Minister Hanna Maliar said Kyiv knew how many soldiers were still at the plant, but stressed that it was "sensitive information".
On Monday, 264 fighters - many badly wounded - were evacuated to areas held by Russian-backed rebels.
On Tuesday, another seven buses were seen leaving the site, Reuters said.
It added that the convoy later arrived in Olenivka, a village held by pro-Russian rebels in the eastern Donbas region.
Russian prosecutors said they would question all the Ukrainian soldiers as part of an investigation into what Moscow describes as "Ukrainian regime crimes against Donbas civilians".
Ukraine wants its troops - the last defenders of the southern port city - to be exchanged for captured Russian soldiers as part of an evacuation deal confirmed by Moscow.
Hundreds of Ukrainian soldiers - Marines, the National Guard (including the Azov regiment), border guards, police and territorial defence units - as well as a number of civilians with young children have been holed up at the site since advancing Russian troops encircled Mariupol in early March.
Earlier this month, dozens of civilians were evacuated from Mariupol to both Russia-controlled and Ukraine-controlled territory.
At Tuesday's briefing in Kyiv, Ms Maliar said only that "we know this number" when asked about how many Ukrainian fighters were still at the Azovstal site.
The sprawling four-square-mile complex is a maze of tunnels designed to survive a nuclear war.
"We understand the scope of the rescue operation, but it is also sensitive information, and it will not be disclosed until the rescue operation is completed," she added.
Describing the fighters as "our heroes", Ms Maliar stressed that the operation was the only way to save them, adding that a "military deblockade" was simply impossible.
In his video address on Tuesday, Ukrainian President Volodymyr Zelensky said Ukrainian military, intelligence and negotiating teams, as well as the Red Cross and the UN, were involved in the evacuation operation. "Ukraine needs its heroes alive," he said.
However, he cautioned that the Ukrainian troops might not be freed immediately and warned that negotiations over their release would require "delicacy and time".
Ukrainian MP Lesia Vasylenko told the BBC it was essential that the deal struck with Russia, with the help of the Red Cross and the UN, went through and the soldiers were exchanged. Otherwise, she said, "the fate of these very brave men will be absolutely unknown and will be in Russian hands, which is far from an ideal situation".
Russian President Vladimir Putin said Ukrainian soldiers evacuated from the steel plant would be treated "in line with the relevant international laws".
However, Russia's lawmakers on Tuesday put forward plans to declare Azov regiment fighters "Nazi criminals" who must not be part of any prisoner swap with Ukraine.
The Azov regiment, set up as a volunteer militia in 2014 but now a National Guard unit, once had links to the far right.
Meanwhile, the office of Russia's prosecutor general has asked the country's Supreme Court to declare the unit a "terrorist organisation" in an apparent attempt to prevent its fighters being treated as conventional prisoners of war.
In a separate development, both Ukraine and Russia on Tuesday admitted that peace talks were currently on hold, blaming each other for this.
MARCH 22: There are four main reasons why taking the port city would be such a strategic win for Russia - and a major blow for Ukraine.
1. Securing a land corridor between Crimea and Donbas
Geographically, the city of Mariupol occupies only a tiny area on the map but it now stands obstinately in the way of Russian forces who have burst out of the Crimean peninsula.
They are pushing north-east to try to link up with their comrades and Ukrainian-separatist allies in the Donbas region of eastern Ukraine.
General Sir Richard Barrons - former commander of UK Joint Forces Command - says capturing Mariupol is vital to Russia's war effort.
"When the Russians feel they have successfully concluded that battle, they will have completed a land bridge from Russia to Crimea and they will see this as a major strategic success."
If Mariupol was seized, Russia would also end up with full control of more than 80% of Ukraine's Black Sea coastline - cutting-off its maritime trade and further isolating it from the world.
By holding out against advancing forces for the past three weeks, the defending Ukrainians have managed to preoccupy a large number of Russian troops. But that failure by Russia to secure a rapid capture of the city, has prompted Russian commanders to resort to a 21st Century version of mediaeval siege tactics.
They have pummelled Mariupol with artillery, rockets and missiles - damaging or destroying over 90% of the city. They have also cut off access to electricity, heating, fresh water, food and medical supplies - creating a man-made humanitarian catastrophe which Moscow now blames on Ukraine for refusing to surrender by an 05:00 deadline on Monday. A Ukrainian MP has accused Russia of "trying to starve Mariupol into surrender".
Ukraine has vowed to defend the city down to the last soldier. It may well come to that. Russian troops are slowly pushing into the centre and, in the absence of any kind of workable peace deal, Russia is now likely to intensify its bombardment - drawing little if any distinction between its armed defenders and the beleaguered civilian population which still numbers over 200,000.
If, and when, Russia takes full control of Mariupol this will free up close to 6,000 of its troops - organised into 1,000-strong battalion tactical groups - to then go and reinforce other Russian fronts around Ukraine.
There are a number of possibilities as to where they could be redeployed:
-to the north-east to join the battle to encircle and destroy Ukraine's regular armed forces fighting pro-Kremlin separatists in the Donbas region
-to the west to push towards Odesa, which would be Ukraine's last remaining major outlet to the Black Sea
-to the north-west towards the city of Dnipro
2. Strangling Ukraine's economy
Mariupol has long-been a strategically important port on the Sea of Azov, part of the Black Sea.
With its deep berths, it is the biggest port in the Azov Sea region and home to a major iron and steel works. In normal times, Mariupol is a key export hub for Ukraine's steel, coal and corn going to customers in the Middle East and beyond.For eight years now, since Moscow's illegal annexation of Crimea in 2014, the city has been sandwiched uncomfortably between Russian forces on that peninsula and the pro-Kremlin separatists in the breakaway self-declared republics of Donetsk and Luhansk.
Losing Mariupol would be a major blow to what is left of Ukraine's economy.
3. Propaganda opportunity
Mariupol is home to a Ukrainian militia unit called the Azov Brigade, named after the Sea of Azov which links Mariupol to the rest of the Black Sea. The Azov Brigade contains far-right extremists including neo-Nazis.
Although they form only the tiniest fraction of Ukraine's fighting forces, this has been a useful propaganda tool for Moscow, giving it a pretext for telling Russia's population that the young men it has sent to fight in Ukraine are there to rid their neighbour of neo-Nazis.If Russia manages to capture alive significant numbers of Azov Brigade fighters it is likely they will be paraded on Russian state-controlled media as part of the ongoing information war to discredit Ukraine and its government.
4. Major morale boost
The capture of Mariupol by Russia, if it happens, will be psychologically significant for both sides in this war.
A Russian victory in Mariupol would enable the Kremlin to show its population - through state-controlled media - that Russia was achieving its aims and making progress.
For President Putin, for whom this war appears to be personal, there is a historical significance to all this. He sees Ukraine's Black Sea coastline as belonging to something called Novorossiya (New Russia) - Russian lands that date back to the 18th Century empire.
Putin wants to revive that concept, "rescuing Russians from the tyranny of a pro-western government in Kyiv" as he sees it. Mariupol currently stands in the way of him achieving that aim.
But to Ukrainians, the loss of Mariupol would be a major blow - not just militarily and economically - but also to the minds of the men and women fighting on the ground, defending their country. Mariupol would be the first major city to fall to the Russians after Kherson, a strategically much less important city that was barely defended.
There is another morale aspect here and that is of deterrence.
Mariupol has put up fierce resistance - but look at the cost. The city is decimated, it lies largely in ruins. It will go down in history alongside Grozny and Aleppo, places that Russia eventually bombed and shelled into submission, reducing them to rubble. The message to other Ukrainian cities is stark - if you choose to resist like Mariupol did then you can expect the same fate.
"The Russians couldn't walk into Mariupol," says Gen Sir Richard Barrons, "they couldn't drive in with their tanks, so they've pounded it to rubble. And that's what we should expect to see anywhere else that really matters to them."
MARCH 21: Under Russia's proposal, civilians would be allowed to leave if the city's defenders laid down arms.
But Ukraine has refused, saying there was no question of it surrendering the strategic port city.
Around 300,000 people are believed to be trapped there with supplies running out and aid blocked from entering.
Residents have endured weeks of Russian bombardment with no power or running water.
Details of the Russian proposal were laid out on Sunday by Gen Mikhail Mizintsev, who said Ukraine had until 05:00 Moscow time (02:00 GMT) on Monday morning to accept its terms.
Under the plans, Russian troops would have opened safe corridors out of Mariupol from 10:00 Moscow time (07:00 GMT), initially for Ukrainian troops and "foreign mercenaries" to disarm and leave the city.
After two hours, Russian forces say they would then have allowed humanitarian convoys with food, medicine and other supplies to enter the city safely, once the de-mining of the roads was complete.
Russian Gen Mizintsev admitted that a terrible humanitarian catastrophe was unfolding there - and said the offer would have allowed civilians to flee safely to either the east or west.
In response to the offer, Ukraine's Deputy Prime Minister Iryna Vereshchuk said Ukraine would not stop defending Mariupol.
"There can be no question of any surrender, laying down of arms," she was quoted by Ukrainska Pravda as saying.
Earlier on Sunday, Pyotr Andryushenko, who is an adviser to the mayor of Mariupol, vowed the city's defenders would fight on.
"We will fight until the last of our soldiers," he said.
He told the BBC's Newshour that Moscow's humanitarian promises could not be trusted, and repeated unconfirmed claims made by Mariupol officials in recent days that Russian forces have been forcibly evacuating some of its residents to Russia.
"When they [Russian forces] say about humanitarian corridors, what do they really do? They really force evacuate our people to Russia," Andryushenko said.
The BBC has not been able to verify these accusations.
Mariupol is a key strategic target for Russia and has seen some of the invasion's deadliest fighting.
Russian troops have encircled the city over the past few weeks, trapping its residents inside without access to electricity, water or gas.
Communication with civilians unable to leave is limited but food and medical supplies are believed to be running out and Russia has blocked any humanitarian aid from getting in.
Since the invasion began the port city has witnessed some of the most intense fighting in all of Ukraine, with Russian forces so far failing to take the city from its defenders.
According to one estimate, 90% of the city's buildings have been damaged or destroyed in attacks since the war began three weeks ago, and authorities say at least 2,500 people have been killed although the true figure may be higher.
After last week's destruction of a theatre where more than 1,000 people were sheltering, on Sunday authorities in Mariupol said that an arts school with 400 people inside has also been attacked.
Previous efforts to evacuate Mariupol's civilians have been blocked by Russian fire, although local authorities say that thousands have been able to leave in private vehicles.
On Sunday, the Ukrainian deputy prime minister said 3,985 people had fled from Mariupol to Zaporizhzhia, adding that on Monday the government plans on sending about 50 buses to pick up further evacuees from the city.
President Volodomyr Zelensky has said the Russian siege amounts to a "war crime".
"This is a totally deliberate tactic," he said. "They [Russian forces] have a clear order to do absolutely everything to make the humanitarian catastrophe in Ukrainian cities an 'argument' for Ukrainians to cooperate with the occupiers".
The location of the port city, on the Sea of Azov, makes it a strategic target for Russia, as it would help it create a land corridor between the eastern regions of Donetsk and Luhansk, controlled by Russian-backed separatists.
The Russian military has offered the Ukrainian troops defending the strategic port of Mariupol to lay down arms and exit the city via humanitarian corridors, but that proposal was quickly rejected by the Ukrainian authorities.
Russia demanded that Ukrainians in the besieged city of Mariupol lay down their arms Monday in exchange for safe passage out of town, but Ukraine rejected the offer.
MARCH 6: Russian forces continued to shell the city of Mariupol on Saturday, despite agreeing to a ceasefire just hours earlier - throwing an attempted mass evacuation of civilians into chaos as Russia and Ukraine war enters day 10.
Despite West's senctions Russia is continously operating its military operations in Ukraine in the bid to take control over Kyiv, the capital city. Destructions are massive and millions have already fled the country.
Here are some recent pictures taken from BBC:
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