Russia has given Ukrainian fighters still holding out in Mariupol a fresh ultimatum to surrender as it pushes for a decisive victory in its new eastern offensive, while Western governments pledged more military help to Kyiv.

Thousands of Russian troops backed by artillery and rocket barrages were advancing on Wednesday in what Ukrainian officials have called the Battle of the Donbas.

Russia’s nearly eight-week-long invasion has failed to capture any of Ukraine’s largest cities, forcing Moscow to refocus in and around separatist regions.

The biggest attack on a European state since 1945 has, however, driven nearly five million people to flee abroad and reduced cities to rubble.

Russia was hitting the Azovstal steel plant, the main remaining stronghold in Mariupol, with bunker-buster bombs, a Ukrainian presidential adviser said late on Tuesday (local time). Reuters could not verify the details.

After an earlier ultimatum to surrender lapsed and as midnight approached, Russia’s defence ministry said not a single Ukrainian soldier had laid down their weapons and it renewed the proposal. Ukrainian commanders have vowed not to surrender.

“Russia’s armed forces, based purely on humanitarian principles, again propose that the fighters of nationalist battalions and foreign mercenaries cease their military operations from 1400 Moscow time on 20th April and lay down arms,” the Russian Defence Ministry said.

The US, Canada and Britain said they would send more artillery weaponry, and the White House said new sanctions were being prepared.

US President Joe Biden is expected to announce a military aid package about the same size as last week’s $US800 million ($A1.1 billion) one in the coming days, sources told Reuters.

UN Secretary-General Antonio Guterres called for a four-day humanitarian pause in the fighting this coming weekend, when Orthodox Christians celebrate Easter, to allow civilians to escape and humanitarian aid to be delivered.

Russia’s war in Ukraine is to blame for exacerbating “already dire” world food insecurity, with price and supply shocks adding to global inflationary pressures, US Treasury Secretary Janet Yellen said.

Russia says it launched what it calls a “special military operation” on February 24 to demilitarise and “denazify” Ukraine. Kyiv and its Western allies reject that as a false pretext.

Ukraine said the new assault had resulted in the capture of Kreminna, an administrative centre of 18,000 people in Luhansk, one of the two Donbas provinces.

Russian Foreign Minister Sergei Lavrov confirmed that “another stage of this operation is beginning”.

Driven back by Ukrainian forces in March from an assault on Kyiv in the north, Russia has instead poured troops into the east for the Donbas offensive.

In Mariupol, scene of the war’s heaviest fighting and worst humanitarian catastrophe, about 120 civilians living next to the Azovstal steel plant left via humanitarian corridors, the Interfax news agency said on Tuesday, quoting Russian state TV.

Mariupol has been besieged since the war’s early days. Tens of thousands of residents have been trapped and Ukraine believes more than 20,000 civilians have died there.

“The Russian army will forever inscribe itself in world history as perhaps the most barbaric and inhuman army in the world,” Ukrainian President Volodymyr Zelenskiy said.

“Deliberately killing civilians, destroying residential quarters and civilian infrastructure, and using all kinds of weapons, including those prohibited by international conventions, is already the brand signature of the Russian army,” he added in a video address.

– AAP