Ukraine launched air strikes and a paratrooper assault against pro-Russian rebels who seized an airport yesterday, 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 Sunday's election behind Petro Poroshenko, a political veteran and billionaire owner of chocolate factories, hoping the 48-year-old can rescue the nation from the brink of bankruptcy, civil war and dismemberment by its former Soviet masters.

Yesterday'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.

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Even as fighting was 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: "These are simply bandits. Nobody in any civilised state will hold negotiations with terrorists."

Gunfire and explosions sounded as a warplane flew over Donetsk's Sergei Prokofiev International Airport, hours after truckloads of rebel fighters seized a terminal.

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 concrete and glass terminal. 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 one 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.

Preliminary results with more than three quarters of votes counted gave Poroshenko 54 per cent of the vote. His closest challenger, former premier Yulia Tymoshenko, secured just 13.1 per cent.

"I hope Russia will support efforts to tackle the situation in the east," Poroshenko said, adding he planned to meet Russian officials in the first half of June.

But he showed no sign of heeding Moscow's demand that he call off the operation against rebels.

"Protecting people is one of the functions of the state," he said.

So far, Ukraine's military forces have had little success against rebels. Officials say they have held back from using full force to avoid provoking an invasion from Russian troops massed on the frontier.

The Ukrainian joint forces' security operation in the region said a deadline for the rebels to surrender expired and two Sukhoi Su-25 jets carried out strafing runs, firing warning shots. A MiG-29 jet later carried out another air strike.

The militants then spread out across the territory of the airport, whose state-of-the-art main terminal was built for the 2012 European soccer championships in Ukraine.

"Right now at the airport, paratroopers have landed and are cleaning up the area," said a Ukrainian security spokesman.

Russian President Vladimir Putin promised at the weekend that Moscow would respect the will of Ukrainians, and Foreign Minister Sergei Lavrov repeated that promise yesterday in saying Russia was ready for dialogue with Poroshenko.