Ukrainian government and rebel forces are both claiming control of the small town of Ilovaisk in the Donetsk region after fierce fighting.
Security forces said the town was under government control but the rebels said they had repulsed an attack.
Nine Ukrainian soldiers died overnight, officials said, including an American with Ukrainian citizenship.
Fighting across the Donetsk region left 34 civilians dead and 29 injured on Tuesday alone, local officials say.
Civilians in the region are also facing mounting problems with supplies of essential goods.
Pro-Russian separatists in the Donetsk and Luhansk regions declared independence from Kiev and proclaimed their own people's republics after Russia annexed the Crimean peninsula from Ukraine in March.
More than 2,000 civilians and combatants have been killed since mid-April, when Ukraine's government sent troops to put down the rebel uprising.
Ukraine accuses Russia of arming the rebels and sending Russian soldiers into eastern Ukraine - a claim denied by the Kremlin.
In another development, several people scaled one of Moscow's "Stalin skyscrapers" to place a Ukrainian flag on top of its star, which they painted yellow and blue, the colours of the Ukrainian flag; police later made several arrests.
Tanks and artillery
Ilovaisk, a town of 16,000 people, lies to the south-east of the city of Donetsk and is an important railway junction. Ukrainian forces have been trying to drive a wedge between the rebels in Donetsk and those in Luhansk region, further east.
Regular troops and volunteer battalions have fought off three counter-attacks by the rebels since entering Ilovaisk on Monday evening, the national guard said in a statement on its website.
The rebels were using artillery and tanks, it said.
Among those killed was a Ukrainian-American known by the nom de guerre of "Franko", said Anton Herashchenko, an adviser to the Ukrainian interior minister.
Franko, he said, was an American citizen with a military background who had been living in eastern Ukraine for the past 10 years and had obtained Ukrainian citizenship.
Rebel news agency Novorossia said that government attempts to capture Ilovaisk, as well as the town of Torez further east and the village of Yasynuvata north of Donetsk, had been repulsed in fierce fighting.
Reporting on the situation in Luhansk region, it said that government forces had continued shelling rebel positions in the suburbs of Luhansk city but had not launched any new offensives.
'Hunger in Donetsk'
The figures for civilian casualties in Donetsk were given by the region's official administration. Both sides in eastern Ukraine have been accused of killing or injuring civilians through indiscriminate use of heavy weapons.
It is one of the highest death tolls in the conflict so far and it underlines concerns that Ukraine's conflict is exacting a heavy toll on the local population, the BBC's David Stern reports from the Ukrainian capital, Kiev.
The deputy prime minister of the self-proclaimed Donetsk People's Republic, Andrei Purgin, has been quoted by Russian media as saying that people are now going hungry in the region after local shops ran out of food and medicine.
Water supplies have been disrupted and there are serious problems with power, Mr Purgin reportedly told a radio station, adding that some two million people were trapped in the besieged city and its hinterland as there were no humanitarian corridors they could use to escape.
Residential areas have been damaged by shelling in recent weeks, with civilians killed.
The situation is much worse, however, in the city of Luhansk where there has been no running water, power or phone connections for 18 days, according to the city council.
Fighting in the city continued overnight, it said, with damage to residential and other buildings.
Meanwhile, the controversial Russian humanitarian aid convoy for Luhansk remains parked a couple of hours' drive away, over the border with Russia, as negotiations continue over its delivery.
Eastern Ukraine - the increasing human cost
- At least 2,119 people have been killed and 5,043 wounded since mid-April, according to a UN report on 7 August
- 951 civilians have been killed in Donetsk region alone, the official regional authorities said on 20 August
- Official casualty counts only record certified deaths while in some particularly dangerous parts of the war zone, such as Luhansk region, victims are said to have been buried informally, for instance in gardens
- Rebels (and some military sources) accuse the government of concealing the true numbers of soldiers killed
- 155,800 people have fled elsewhere in Ukraine while at least 188,000 have gone to Russia