The battle for the main transport hub in the rebel-held east erupted yesterday, in a sharp escalation of the conflict after president-elect Petro Poroshenko vowed to take a tough stand against the "terrorists".
"The airport is under our full control. The enemy suffered heavy losses. We have none," Interior Minister Arsen Avakov said in a statement.
He said however that the military was continuing its operation at the airport, and AFP journalists reported hearing explosions and heavy gunfire during the morning.
An AFP correspondent reported seeing body parts and blood splattered near a bullet-riddled truck on the airport road, where makeshift blockades had been set up with dumper trucks and piles of tyres.
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In Moscow, Russian Foreign Minister Sergei Lavrov called for all sides to halt the violence.
"The number one task for the Kiev authorities and the test of their durability, taking into consideration the results of the presidential election is bringing an immediate end to the use of the army against the public and an end to any violence by all sides," Lavrov said.
The strikes represented the most forceful action by Kiev in its battle to crush a bloody pro-Moscow rebellion that has raged in the coal and steel belt since early April, threatening to tear apart the former Soviet state.
The fighting flared on the very day that billionaire oligarch Poroshenko was formally declared the winner of Sunday's presidential election with 54 per cent of the vote.
The 48-year-old pledged to work to restore stability in Ukraine after months of turmoil and rebuild relations with Russia while steering the country on a westward path.