* Ukrainian soldiers, many wounded, bussed to Russian-held towns

* Mariupol a win for Putin as Russian forces fall back elsewhere

* Russia, Ukraine differ in views on potential prisoner exchange

* Finland, Sweden set to file NATO applications

MARIUPOL, Ukraine, May 18

Concerns grew on Wednesday for the welfare of more than 250 Ukrainian fighters who surrendered to Russian forces at the Azovstal steelworks in Mariupol after weeks of desperate resistance.

The surrender brought an end to the most devastating siege of Russia's war in Ukraine and allowed President Vladimir Putin to claim a rare victory in his faltering campaign, which many military analysts say has stalled.

Buses left the steelworks late on Monday in a convoy escorted by Russian armoured vehicles. Five arrived in the Russian-held town of Novoazovsk, where Moscow said wounded fighters would be treated.

Seven buses carrying Ukrainian fighters from the Azovstal garrison arrived at a newly reopened prison in the Russian-controlled town of Olenivka near Donetsk, a Reuters witness said.

Russia said at least 256 Ukrainian fighters had 'laid down their arms and surrendered', including 51 severely wounded. Ukraine said 264 soldiers, including 53 wounded, had left.

Russian defence ministry video showed fighters leaving the plant, some carried on stretchers, others with hands up to be searched by Russian troops.

There were some women aboard at least one of the buses in Olenivka, Reuters video showed.

While both sides spoke of a deal under which all Ukrainian troops would abandon the steelworks, many details were not yet public, including how many fighters still remained inside, and whether any form of prisoner swap had been agreed.

The Kremlin said Putin had personally guaranteed the prisoners would be treated according to international standards, and Ukrainian officials said they could be exchanged for Russian captives.

Ukrainian Deputy Prime Minister Iryna Vereshchuk said Kyiv aimed to arrange a prisoner swap for the wounded once their condition stabilised.

Russian Deputy Ambassador to the United Nations Dmitry Polyansky said there had been no deal, tweeting: 'I didn't know English has so many ways to express a single message: the #Azovnazis have unconditionally surrendered.'

TASS news agency reported a Russian committee planned to question the soldiers, many of them members of the Azov Battalion, as part of an investigation into what Moscow calls 'Ukrainian regime crimes'.

High-profile Russian lawmakers spoke out against any prisoner swap. Vyacheslav Volodin, speaker of the State Duma, Russia's lower house, said: 'Nazi criminals should not be exchanged.'

Lawmaker Leonid Slutsky, one of Russia's negotiators in talks with Ukraine, called the evacuated combatants 'animals in human form' and said they should be executed.

Formed in 2014 as an extreme right-wing volunteer militia to fight Russian-backed separatists, the Azov Regiment denies being fascist or neo-Nazi. Ukraine says it has been reformed and integrated into the National Guard.

Natalia, the wife of a sailor among those holed up in the plant, told Reuters she hoped 'there will be an honest exchange'. But she was still worried: 'What Russia is doing now is inhumane.'

BATTLE FOR DONBAS

The denouement of the battle for Mariupol, which came to symbolise Ukrainian resistance, is Russia's biggest victory since it launched what it calls a 'special military operation' to 'denazify' the country on Feb. 24.

It gives Moscow control of the Azov Sea coast and an unbroken stretch of eastern and southern Ukraine. But the port lies in ruins, and Ukraine believes tens of thousands of people were killed under months of Russian bombardment.

On the diplomatic front, U.S. President Joe Biden will host the leaders of Sweden and Finland at the White House on Thursday to discuss their NATO applications, the White House said. The Nordic countries are optimistic they can overcome objections from Turkey over jointing the 30-nation alliance.

Russia's offensive in the east, meanwhile, appeared to be making little progress, although the Kremlin says all its objectives will be reached.

Around a third of the Donbas was held by Russia-backed separatists before the invasion. Moscow now controls around 90% of Luhansk region, but it has failed to make major inroads towards the key cities of Sloviansk and Kramatorsk in Donetsk in order to extend control over the entire Donbas.

Ukrainian forces have advanced at their fastest pace for more than a month, driving Russian forces out of the area around Kharkiv, Ukraine's second-largest city.

Ukraine says its forces had reached the Russian border, 40 km (25 miles) north of Kharkiv. They have also pushed at least as far as the Siverskiy Donets river 40 km to the east, where they could threaten Russian supply lines.

Putin may have to decide whether to send more troops and hardware to replenish his weakened invasion force as an influx of Western weapons, including scores of U.S. and Canadian M777 howitzers that have longer range than their Russian equivalents, bolsters Ukraine's combat power, analysts said.

'Time is definitely working against the Russians ... The Ukrainians are getting stronger almost every day,' said Neil Melvin of the RUSI think-tank in London.