There have been more fierce clashes in eastern Ukraine, where pro-Russian separatists are trying to capture Donetsk airport.
Heavy firing could be heard near the airport - strategically important for both sides in the conflict.
A government spokesman said the rebels had broken into one of the terminals but were later pushed back. The rebels say they have seized the airport.
A truce agreed in eastern Ukraine on 5 September looks increasingly fragile.
On Friday US Secretary of State John Kerry spoke on the phone with his Russian counterpart Sergei Lavrov to "express his concern about intensifying violence in eastern Ukraine".
"Russia must use its influence with the separatists and end these attacks immediately", state department spokeswoman Jen Psaki said.
"The situation in the area of Donetsk airport remains difficult," Ukrainian military spokesman Vladyslav Seleznyov told Ukraine's Kanal 5 TV.
"The militants, using smoke bombs as a cover, broke into the ground floor of the old terminal," he said.
Ukrainian soldiers had pushed the rebels from half the building, Mr Seleznyov added.
But leaders of the self-proclaimed Donetsk People's Republic claimed that their fighters had seized the whole airport.
Eyewitnesses earlier told local media that a number of rebels had been killed during the clashes.
A correspondent for Associated Press news agency reported seeing three rebel tanks firing at the main terminal, with sniper shots ringing out.
Fighting for the airport - a vantage point for the Ukrainian army to fire on positions in rebel-held Donetsk - has intensified in recent days. Ukraine says two servicemen have been killed and another nine wounded since Thursday.
Mr Seleznyov also accused Russia of sending drones over the airport to help the rebels' reconnaissance efforts and direct fire.
Russia has denied sending arms to the rebels or soldiers to eastern Ukraine, though it says "volunteers" have crossed into Ukraine.
Earlier, the International Committee of the Red Cross (ICRC) condemned indiscriminate shelling in east Ukraine after a Red Cross employee was killed.
Swiss citizen Laurent DuPasquier, 38, died when a shell landed near ICRC offices in Donetsk on Thursday.
At the scene: James Coomarasamy, BBC News
I wasn't sure what I had imagined a rebel base would look like, but it wasn't this - the entrance to an unprepossessing apartment block in a densely populated residential area on the edge of Donetsk.
Passing piles of sand bags and a row of gas masks, we were ushered into the strategy room, where a man with a grey ponytail and a burgundy beret was tapping on a computer, pipe in hand.
A large table dominated the room. On it, a series of maps was spread out, showing rebel-held territory. An X marked the spot where, they assured us, a Ukrainian helicopter had been shot down in the past few weeks.
Mr DuPasquier was one of several casualties in the city, ICRC director of operations Dominik Stillhart said in a statement.
The rebels and the government blamed each other for the shelling.
Mortar shells also landed in central Donetsk early on Friday, the BBC's Dina Newman reports from a hotel in the city centre.
The two sides have accused each other of violating the ceasefire.
More than 3,500 people have been killed in the eastern Ukrainian regions of Donetsk and Luhansk since the conflict erupted between the heavily armed separatists and the new Kiev government in April.
In March, Russia annexed Ukraine's southern Crimea peninsula - a move condemned around the world.
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