At least 30 pro-Russia separatists have been killed so far in fighting at the airport in the eastern Ukrainian city of Donetsk, insurgents say.
Armed separatists tried to take over the airport on Monday.
A BBC team near the airport on Tuesday said sporadic gunfire continued, though one Ukrainian military spokesman said it now controlled the facility.
New President Petro Poroshenko vowed on Monday 'anti-terrorist operations' in the east would 'last hours not months'.
A representative of the self-proclaimed Donetsk People's Republic told the BBC that reports of at least 30 dead in Monday's fighting were accurate.
One insurgent told Associated Press the bodies had been brought to a hospital in the city.
Interior Minister Arsen Avakov said there were no casualties among Ukrainian troops.
Monday's clashes started after separatist militants stormed the Sergei Prokofiev Donetsk airport in the early hours of the morning.
The Ukrainian military responded quickly with air strikes and an assault by heavily armed troops.
Reporters said there was heavy gunfire throughout the day and night, with black smoke rising into the air.
President's vow
The attempt to seize the airport may have been intended to prevent Mr Poroshenko from travelling there after he said his first trip in office would be to visit the restive east.
Mr Poroshenko, a 48-year-old billionaire and forme.