Hundreds of Ukrainian fighters, including wounded men carried out on stretchers, left the vast steel plant in Mariupol where they mounted a dogged last stand and turned themselves over to Russian hands, signalling the beginning of the end of a siege that became a symbol of Ukraine's resistance to Moscow's invasion.

Russia on Tuesday called the operation a mass surrender.

The Ukrainians avoided using that word but said the garrison had completed its mission, and that they were working to pull out the fighters that remain.

On Monday, more than 260 fighters left the Azovstal plant, their last redoubt in Mariupol and were transported to two towns controlled by Moscow-backed separatists, officials on both sides said.

Other fighters, their precise numbers unknown, remain inside the ruins of the fortified mill that sprawls over four square miles in the otherwise Russian-held city.

Azovstal's fall would mark the complete capture of Mariupol, a significant milestone in one of the bloodiest battles of the war.

It would give Russia its biggest victory yet after multiple setbacks, both military and diplomatic.

Its troops have suffered costly losses, and President Vladimir Putin is increasingly isolated internationally, with Finland and Sweden announcing in recent days that they intend to join Nato, a major blow to the Russian leader.

Wrapping up Mariupol's capture would give Russia an unbroken land bridge to the Crimean Peninsula, which it annexed from Ukraine in 2014, and also deprives Ukraine of a vital port.

It could also free up Russian forces for fighting elsewhere in the industrial heartland of eastern Ukraine.

But Ukraine sought to turn the evacuation into a symbol for its side, too, highlighting the role that the Azovstal fighters played in boosting Ukrainian morale and tying up Russian forces who could not be deployed elsewhere.

"Ukraine needs Ukrainian heroes to be alive.

"It's our principle," Ukrainian President Volodymyr Zelensky said in announcing that troops had begun leaving the relentlessly bombarded mill and its warren of tunnels and bunkers.

"The work continues to bring the guys home and it requires delicacy and time," he said.

It is not clear what will happen to the fighters - and a Russian official cast doubt over whether Moscow would agree to hand over all of the men in a prisoner of war exchange.

Ukraine deputy defence minister Hanna Maliar said 264 fighters were evacuated from the plant, including 53 "heavily wounded" brought to a medical facility.

Russian defence ministry spokesman Igor Konashenkov gave slightly different numbers: 265 evacuees, 51 of them seriously wounded.

The discrepancy could not immediately be explained.

After nightfall on Monday, several buses pulled away from the mill accompanied by Russian military vehicles.

Russian defence ministry video of some evacuees did not show any that were armed.

In the footage, troops patted down and searched the fighters.

Some were on stretchers as they were loaded onto the buses.

Oleksandr Danylyuk, a Ukrainian former national security chief and finance minister, told the BBC that because Ukrainian forces were unable to liberate the plant, the negotiated evacuation to Russian-controlled territory had been "the only hope" for Azovstal's defenders.

Those remaining in the plant are still "able to defend it.

"But I think it's important to understand that their main mission is completed and now their lives need to be saved", he said.

A full negotiated withdrawal could save lives on the Russian side, too, sparing Russian-backed troops from what almost certainly would be a bloody and difficult battle to wrest the labyrinth-like plant from Ukrainian control.

Mr Danylyuk added that those evacuated should be swapped for Russian prisoners but Vyacheslav Volodin, speaker of the lower house of the Russian parliament, said without evidence that there are "war criminals" among the plant defenders and they should not be exchanged but tried.

Russia has repeatedly falsely portrayed the wider war as a battle against Nazism, and Mr Volodin again levied that accusation.

Ms Maliar, the Ukrainian official, heaped praise on the fighters but said it been impossible to liberate them "by military means".

"Mariupol's defenders have fully accomplished all missions assigned by the commanders," she said.

Retired French Vice Admiral Michel Olhagaray, a former head of France's centre for higher military studies, said Azovstal's fall would be more of a symbolic boost for Russia than a military one.

"Factually, Mariupol had already fallen but not symbolically because of this incredible resistance," he said.

"Now Putin can claim a 'victory' in the Donbas," the eastern Ukrainian region that is now his focus.

But because Azovstal's defenders tied down Russian troops Ukraine can also claim that it came out on top.

"Both sides will be able take pride or boast about a victory - victories of different kinds," he said.

After Russia's failure in the initial stages of the February 24 invasion to take the capital, Kyiv, the focus of the fighting has shifted to the Donbas but also has turned into a slog.

Strikes have also occasionally hit other areas of the country. The western city of Lviv was rocked by loud explosions early Tuesday.

Witnesses counted at least eight blasts accompanied by distant booms.

The sky west of the city, which was under an overnight curfew, was lit up by an orange glow.

The governor of the Lviv region, Maksym Kozytskyy, said Russian strikes targeted railroad and military facilities around Yavoriv, west of the city.

The Yavoriv area, which is just a short drive from Ukraine's border with Poland, has also been the target of previous Russian strikes apparently aimed at slowing the flow of weapons and supplies coming from Western countries.

A Russian strike in March also killed 35 people at Yaroviv military training base.

Howitzers from the US and other countries have helped Kyiv hold off or gain ground against Russia, a senior US defence official said, who spoke on condition of anonymity to discuss the US military assessment.

In another setback for Moscow, Swedish foreign minister Ann Linde signed the formal request to join Nato that will now be sent to the alliance's secretary-general, Jens Stoltenberg.

Sweden's move follows a similar decision by neighbouring Finland, historic shifts for the countries, which have been nonaligned for generations.

US President Joe Biden Biden will host prime minister Magdalena Andersson of Sweden and President Sauli Niinisto of Finland at the White House on Thursday to discuss the two countries' Nato applications.

Mr Stoltenberg has said the membership process for both could be quick but President Recep Tayyip Erdogan of Turkey, a Nato member, has cast doubt on that.

He has objected to allowing Sweden and Finland to join Nato, saying they failed to take a "clear" stance against Kurdish militants and other groups that Ankara considers terrorists, and imposed military sanctions on Turkey.

All 30 current Nato members must agree to let the Nordic neighbours join.

Mr Putin said on Monday that Moscow "does not have a problem" with Sweden or Finland as they apply for Nato membership, but that "the expansion of military infrastructure onto this territory will of course give rise to our reaction in response".