Ukraine launched air strikes and a paratrooper assault against pro-Russian rebels who seized an airport on Monday.

Ukraine launched air strikes and a paratrooper assault against pro-Russian rebels who seized an airport on Monday, as its newly elected leader rejected any talks with "terrorists" and said a robust military campaign in the east should be able to put down a separatist revolt in "a matter of hours".

Ukrainians rallied overwhelmingly in an election on Sunday behind Petro Poroshenko, a political veteran and billionaire owner of chocolate factories, hoping the burly 48-year-old can rescue the nation from the brink of bankruptcy, civil war and dismemberment by its former Soviet masters in the Kremlin.

Monday's rapid military response to separatists who seized the airport in Donetsk was a defiant answer to Moscow, which said it was ready for dialogue with Poroshenko but demanded he first scale back the armed forces' campaign in the east.

Even as the fighting was getting under way, Poroshenko held a news conference in Kiev where he said the government's military offensive needed to be "quicker and more effective".

"The anti-terrorist operation should not last two or three months. It should last for a matter of hours," he said.

As for the rebel fighters: "They want to preserve a bandit state which is held in place by force of arms," he said. "These are simply bandits. Nobody in any civilized state will hold negotiations with terrorists."

Gunfire and explosions could be heard as a warplane flew over Donetsk's Sergei Prokofiev International Airport, hours after truckloads of armed rebel fighters arrived and seized a terminal. Thick black smoke rose from within the perimeter.

The government said its jets had strafed the area with warning shots and then struck a location where rebels were concentrated, scattering the fighters before paratroops were flown in to face them.

After three hours of fighting, a Reuters photographer saw three Ukrainian Mi-24 helicopter gunships fire rockets and cannon at the terminal concrete and glass terminal. More plumes of black smoke shot up into the air as the helicopters fired at targets on the runway. The gunships threw out decoy flares as fighters shot at them from the ground.

The airport serves a city of 1 million people that the rebels have proclaimed capital of an independent "people's republic", and where they succeeded in blocking all voting in Sunday's election.

Their attempt to seize the airport may have been intended to prevent Poroshenko from travelling there: he has said his first trip in office would be to visit the restive east.