Artillery pounded the rebel bastion of Donetsk in southeastern Ukraine on Sunday as the West warned Russia that any attempt to send "humanitarian" troops into the conflict-torn region would be "unacceptable".
In a round of telephone calls late Saturday, US President Barack Obama, German Chancellor Angela Merkel and British Prime Minister David Cameron agreed that any unilateral move by Russia into Ukrainian territory would be seen as "illegal" and "unacceptable".
Russia on Saturday denied an allegation by Kiev that it had tried to send in a convoy disguised as an aid mission.
Shelling meanwhile continued through the night in Donetsk, a city of one million that rebels now say has been surrounded by Ukrainian forces.
There were no reports of casualties however.
- Warning of 'additional consequences' -
Western leaders reacted strongly after Ukraine said it had scuppered a Russian "humanitarian convoy with 'peacekeepers'" moving towards the border, accompanied by troops and military hardware.
"Any Russian intervention in Ukraine... without the formal, express consent and authorisation of the government of Ukraine is unacceptable," Obama and Merkel agreed in a phone call late Saturday.
Such a move "violates international law, and will provoke additional consequences," on top of the many economic sanctions already in place against Moscow, the White House added.
In a separate conversation, Obama and Cameron said that a Russian move into Ukraine would be "unjustified and illegal".
The West has warned for days that Moscow, whom it accuses of backing the separatists, could use the looming humanitarian crisis in eastern Ukraine as a pretext to send in troops.
NATO says Russia has some 20,000 troops on the border with its former Soviet neighbour.
A spokesman of Russian President Vladimir Putin denied Saturday that Moscow tried to enter Ukraine's territory as claimed by Kiev.
Foreign Minister Sergei Lavrov however later telephoned his US counterpart John Kerry, seeking support for an aid mission to southeastern Ukraine.
More than 285,000 people have fled their homes in eastern Ukraine, according to the UN refugee agency UNHCR.
Fighting between government troops and insurgents has also left some 1,300 people dead and more than 4,000 injured in four months of what the Red Cross has already deemed a civil war in the industrial region.
Local authorities in the east are now warning of a looming humanitarian catastrophe, especially in the second largest rebel-held city of Lugansk, where residents have been without power or running water for days, while fuel and food supplies are running short.
Pensions, salaries and social benefits were also not being paid out as many banks in the region are closed, authorities said.
In a phone conversation with Merkel, Ukraine's President Petro Poroshenko said he was ready to accept humanitarian aid for Lugansk and was already in talks with the Red Cross to organise a mission, but only if it is "an international one without any military escort".
- Donetsk under fire -
Donetsk meanwhile came under renewed shelling overnight and on Sunday morning, with city authorities reporting that a home and a clinic in a district north of the centre had been hit, injuring at least one person.
AFP journalists on the ground said they heard more than 20 explosions in the early morning and that the assault was continuing. A maternity hospital had its windows shattered while mothers and babies huddled in the cellar for safety, one AFP journalist reported.
Ukraine's military said in a statement that it was "tightening its grip on Donetsk" although it also reported that several of its positions were still coming under mortar fire from Russian territory.
Heavy fire also continued on Lugansk.
Ukrainian forces have been trying to wrest back control of the main rebel-held cities in the east and cut them off from Russia.
The head of the self-proclaimed Donetsk People's Republic, Alexander Zakharchenko, called Saturday for a ceasefire on humanitarian grounds after admitting the city was surrounded.
But he also pledged that insurgents would fight "for every street, for every house, for every metre of our land" if the Ukrainian army attempted to push into the city.