Ukrainian government troops say they have repelled an attack by pro-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.
Ukrainian PM Arseniy Yatsenyuk: “Russia is a threat to the global order”
Ukraine and Western countries accuse Russia of intervening on the side of pro-Russian rebels in eastern Ukraine. Russia denies this.
On Saturday, Russia’s Foreign Minister Sergei Lavrov described as “nonsense” reports that Russia was intent on creating a buffer zone in eastern Ukraine.
Russia, he said, wanted Ukraine to be a “prosperous, neutral and friendly country”.
And he accused the US of “trying to use the crisis in Ukraine to break economic ties between the EU and Russia and force Europe to buy US gas at much higher prices”.
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.
The BBC’s Paul Adams: “People in Donetsk do not stray far from the bunkers – no one trusts the ceasefire”
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.
The convoy entered Ukraine from the Izvarino customs control checkpoint
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”.
Mr Yatsenyuk’s comments come after the US government imposed new sanctions on major Russian banks, defence and energy companies.
The sanctions, announced on Friday, mean that US citizens will not be able to provide loans lasting longer than 30 days to Sberbank, Russia’s biggest bank.
The measures are part of a joint effort between Ukraine and the European Union, aimed at punishing Russia for what they say is its military intervention in Ukraine.
The Russian foreign ministry denounced the new sanctions as “another hostile step in line with the confrontational course” taken by the US, and promised retaliatory measures.
The US sanctions block support or technology for Arctic and offshore exploration by five Russian energy firms – Gazprom, Lukoil, Rosneft, Surgutneftegaz and Transneft.
Rosneft was already listed under a previous round of sanctions and is included in the EU sanctions list.
Russia has ambitious plans for Arctic oil exploration. Western partners including ExxonMobil and BP are already involved in multi-billion-dollar projects in Siberia.
The EU sanctions also block the export of oil services and deep-water technology. Transneft is also on the EU list, along with Gazprom Neft, the oil unit of gas giant Gazprom.
Their access to financial markets will be restricted – a serious matter for Rosneft, which last month asked the Russian government for a $42bn (£25.2bn) loan.
In the EU and US, big Russian state-owned banks are now barred from getting loans with a maturity longer than one month.
More than 100 top Russian officials and rebel leaders in Ukraine are also subject to EU and US visa bans and asset freezes.