A Russian ultimatum to Ukrainian troops in Mariupol to surrender or die expired on Wednesday afternoon with no mass capitulation, but the commander of a unit believed to be holding out in the besieged city said his forces could survive just days or hours.

The United Nations said on Wednesday the number of refugees who have fled Ukraine since Russia invaded on Feb 24 had exceeded five million. More than half are children.

Ukraine said it had so far held off an assault by thousands of Russian troops attempting to advance in what Ukrainian officials call the Battle of the Donbas, a new campaign to seize two eastern provinces Moscow claims on behalf of separatists.

In a video, the commander of Ukraine's 36th Marine Brigade, one of the last units believed to be holding out in Mariupol, asked for international help to escape the city's siege.

"This is our appeal to the world. It may be our last. We may have only a few days or hours left," said Major Serhiy Volyna in a video uploaded to Facebook. "The enemy units are dozens of times larger than ours, they have dominance in the air, in artillery, in ground troops, in equipment and in tanks."

Volyna spoke in front of a white brick wall in what sounded like a crowded room. Reuters could not verify where or when the video was filmed or who else might have been there.

Russia's nearly eight-week-long invasion has failed to capture any of Ukraine's largest cities. Moscow was forced to retreat from northern Ukraine after an assault on Kyiv was repelled last month, but has poured troops back in for an assault on the east that began this week.

In the ruins of Mariupol, site of the war's heaviest fighting and worst humanitarian catastrophe, Russia was hitting the last main Ukrainian stronghold, the Azovstal steel plant, with bunker-buster bombs, Kyiv said. Ukrainian officials have said women and children are trapped in bunkers under the plant.

"The world watches the murder of children online and remains silent," presidential adviser Mykhailo Podolyak wrote on Twitter.

Russia has been trying to take full control of Mariupol since the war's first days. Its capture would be a big strategic prize, linking territory held by pro-Russian separatists in the east with the Crimea region that Moscow annexed in 2014.

Russian-backed separatists said shortly before a 2 p.m. (1100 GMT) Wednesday deadline that just five people had surrendered. The previous day, Russia said no one had responded to a similar surrender demand.

Ukraine announced plans to send 90 buses to evacuate 6,000 civilians from Mariupol, saying it had reached a "preliminary agreement" with Russia on a safe corridor, for the first time in weeks. But none of those earlier agreements have actually succeeded on the ground, with Moscow blocking all convoys.

Once a prosperous port of 400,000 people, Mariupol has been reduced to a blasted wasteland with corpses in the streets and residents confined to cellars. Ukrainian officials say tens of thousands of civilians have died there.

U.N. data showed that 5.03 million had fled Ukraine as of Wednesday, bringing the tally above 5 million for the first time.

"They have left behind their homes and families," refugee agency UNHCR head Filippo Grandi said on Twitter. "...Every new attack shatters their hopes. Only an end to the war can pave the way for rebuilding their lives."

BATTLE OF DONBAS

The battle for the Donbas region, which includes the provinces Luhansk and Donetsk, could be decisive as Russia searches for a victory to justify President Vladimir Putin's Feb. 24 invasion. Putin says Ukraine mistreated Russian-speakers in the Donbas, an accusation Kyiv dismisses as false.

Russian television showed Putin addressing a girl from Luhansk on Wednesday: "It was the tragedy that took place in the Donbas, including in the Lugansk People's Republic, that forced, simply forced Russia to launch this military operation, which everyone is well aware of today," he said.

Ukrainian presidential advisor Oleksiy Arestovych said Russia was focusing on advancing towards the strategically important Donbas city of Sloviansk, but "so far they are not succeeding". Targeting that area from several directions is part of an apparent effort to surround Ukrainian forces in the east.

Ukraine's Defence Minister Oleksii Reznikov tweeted that Russia’s "military capacity has been significantly diminished" since the start of the war. "We’re defeating & will continue to defeat the occupiers!"

Peace talks have been stalled. The Kremlin accused Kyiv of delaying the talks and changing its positions. Kyiv accuses Moscow of blocking talks by refusing humanitarian ceasefires, especially to relieve besieged Mariupol.

British military intelligence said fighting in the Donbas was intensifying as Russian forces tried to break through Ukraine's lines, and that Russia was still building up forces on Ukraine's eastern border.

Moscow is hoping its advantage in firepower will give it more success against Ukrainian defenders than in the failed campaign against Kyiv, when its overstretched supply lines were attacked by nimble small units.

Within a day of launching the Donbas offensive, Russian forces captured Kreminna, a frontline town of 18,000 people, on Tuesday. Ukraine's general staff said Russian forces had attempted an offensive near Kharkiv, the country's second biggest city, close to Russia's supply lines to Donbas.

Charles Michel, head of the European Council that groups the 27 EU member states, arrived in Kyiv as the latest European official to visit and demonstrate support.

In the latest sign of Russia's international isolation, sports industry news site Sportico reported that Russian players would be banned from the Wimbledon tennis tournament.

The All England Lawn Tennis Club, which organises the grand slam event, did not immediately respond to a request for comment. Kremlin spokesperson Dmitry Peskov said: "To make sports people hostages of political intrigue is unacceptable."

(Reporting by Natalia Zinets in Ukraine and Reuters journalists; Writing by Peter Graff; Editing by Himani Sarkar and Philippa Fletcher)