Ukrainian government troops say they have repelled an attack bypro-Russian rebels on Donetsk airport.
All Saturday morning gunfire was heard from the area, controlled by government forces despite rebel victories in the rest of the eastern city.
Correspondents say the fresh violence is a big challenge to a fragile ceasefire agreed on 5 September.
Meanwhile Ukrainian Prime Minister Arseniy Yatsenyuk has accused Russia of wanting to "eliminate" his country.
He said Ukraine was "in a stage of war", with the "key aggressor" being Russia.
Mr Yatsenyuk said the goal of Russian President Vladimir Putin "is to take the entire Ukraine", adding that Nato was the "only vehicle" that could protect his country.
Ukraine and Western countries accuse Russia of intervening on the side of pro-Russian rebels in eastern Ukraine. Russia denies this.
Russian convoy The BBC's Paul Adams, in Donetsk, says most of the gunfire around the airport sounded like artillery, but that multiple rocket launchers have also been in use.
On Friday night, he also heard a volley fired from somewhere much closer to the centre of the city.
There are additional reports of plumes of black smoke rising above the airport.
A couple of hundred Ukrainian army troops have been holed up at the airport since June - but our correspondent says that something more concerted now appears to be going on there.
Also on Saturday morning, Russian customs officials said that a Russian aid convoy had crossed into eastern Ukraine.
A spokesman for the European security watchdog, the OSCE, told our correspondent that 220 Russian lorries had passed the border overnight and on Saturday morning - the majority of which were not inspected by either Ukraine or international observers.
Kiev and Western officials fear such convoys may contain military equipment to help the rebels, but Russia insists they contain essential humanitarian supplies such as generators, food and drink.
A similar convoy entered the country last month without Ukraine's permission, sparking condemnation from the US and the EU.
Nato says Russia still has about 1,000 heavily armed troops in eastern Ukraine and about 20,000 more near the border.
Russia denies sending direct military help to the rebels, insisting that any Russian soldiers there are "volunteers".