A military truck with armed militants drives through a police checkpoint toward Donetsk International Airport in eastern Ukraine on Monday. Reuters journalists near the airport heard gunfire and explosions in the vicinity and saw smoke billowing from inside the perimeter as fighter jets flew overhead on Monday. Yannis Behrakis / Reuters

Military claims control of Donetsk airport after airborne raid on rebels

Separatist rebels in eastern Ukraine reported heavy casualties on Tuesday after a second day of fighting with government forces, as authorities in Kiev vowed to continue the military offensive "until not a single terrorist" was left.

The surge in violence began on Monday, as billionaire chocolate magnet Petro Poroshenko claimed victory in Ukraine's presidential election, promising that the eastern uprising would be crushed in "a matter of hours".

A representative for the militants conceded that about 30 rebels had been killed by Tuesday, while Alexander Lukyanchenko, the mayor of Donetsk, said the death toll stood at 40, including two civilians.

A Reuters correspondent counted 20 bodies in combat fatigues in one room of a city morgue, some of them missing limbs.

Ukraine used airstrikes and a paratroop assault on Monday to clear rebels from Donetsk's international airport and had pushed the separatists out of the complex by the end of the day.

But shooting continued through the night, and on Tuesday the road to the airport bore signs of fighting overnight and heavy machinegun fire could be heard in the distance in mid-morning.

"The airport is completely under control," Interior Minister Arsen Avakov told journalists in Kiev. "The adversary suffered heavy losses. We have no losses," he added.

"We'll continue the anti-terrorist operation until not a single terrorist remains on the territory of Ukraine," First Deputy Prime Minister Vitaly Yarema said on the margins of a government meeting.

Military offensive

Ukraine launched the fresh offensive against the rebels, who have occupied strategic points in Donetsk, an industrial hub of 1 million, and other towns in the east, after Kiev's newly elected leader rejected any talks with "terrorists".

Poroshenko, a 48-year-old billionaire, won overwhelming support in Sunday's election that many hoped would draw a line under six months of upheaval. He said a robust military campaign in the east should be able to put down the separatist revolt quickly.

On the road to the airport, Reuters journalists saw blood-spattered and bullet-riddled hulks of trucks of the kind the separatist fighters have been using.

Though the rebels backing the self-proclaimed Donetsk People's Republic had suffered serious losses, the heavy machine gunfire indicated that government forces were still facing resistance.