Russian reports say Ukrainian President Petro Poroshenko has rejected a peace plan sent to him in a letter from Russian President Vladimir Putin.
Russian media say the plan calls on Ukraine's military and the separatists to immediately pull back their heavy weapons to the lines spelled out in a September cease-fire agreement.
But the Russian media reports say a Putin spokesman said Poroshenko rejected the plan and resumed shelling.
There has been no comment from the Ukrainian president, who Sunday addressed thousands of marchers in Kyiv. They were paying tribute to the 13 people killed last week when a shell hit their bus near the town of Volnovakha, about 60 kilometers southwest of Donetsk.
Poroshenko said his government will not give away one scrap of Ukrainian land.
Also Sunday, Ukraine's military said it cleared pro-Russia rebels from much of the Donetsk airport.
"The decision was taken for a mass operation, which was successful. As you saw the information yesterday, we succeeded in almost completely cleaning the territory of the airport, which belongs to the territory of Ukrainian forces as marked by military separation lines, and it is not a violation of Minsk agreements, because Ukrainian soldiers stay in their positions, they adhere to the cease-fire regime, and they shoot only in return," said a spokesman.
Four soldiers were killed and dozens wounded. Fighting for control of the nearly destroyed airport began months ago.
The United Nations Secretary-General Ban Ki-moon said he was "alarmed" by the severe escalation of fighting. He urged an immediate and full cessation of hostilities.
In recent weeks, fighting between Ukrainian forces and Russian-backed separatists in eastern Ukraine has intensified, making compliance with last September's truce more and more remote.
A peace march Sunday in Kyiv drew thousands of people to the streets of the capital to pray for peace and to honor civilian victims of the conflict in eastern Ukraine.
Accompanied by top government officials, President Petro Poroshenko told a crowd of several thousand gathered that Ukraine wouldn't "give up an inch" of its land to Russian-backed separatists.
Poroshenko also spoke of the victims of last week's rocket strike on a commuter bus in Volnovakha, south of Donetsk, that killed 13 people, the worst single loss of civilian life since a September truce.
Many of the marchers carried "I am Volnovakha" signs akin to those seen last week throughout Europe and other parts of the world at solidarity rallies condemning the Charlie Hebdo terror attacks in Paris.
The World Health Organization says more than 4,800 people have been killed in Ukraine's conflict since April 2014, between Kyiv's forces and separatists, who Ukraine and the West say are supported and armed by Russia. Moscow denies the claim.