After a heavy military assault that killed at least 50 rebels Ukraine claimed victory over pro-Russia separatists who seized the Donetsk airport, but warned a showdown was looming as hundreds of Russian fighters had crossed borders to help the dissidents.

After taking control of the airport by unleashing the most aggressive military action against the separatists so far, Kiev ordered the fighters occupying the Donetsk regional administration building to surrender.

"We have posed another ultimatum to them, and if they do not surrender, we will strike them with special weapons," Vladislav Seleznev, a government spokesman, said in Kiev.

Ukraine's foreign ministry said several truckloads of Russian fighters have crossed into the eastern parts of the country, and blamed Russia for failing to stop them.

In the Luhansk region Ukrainian border guards stopped dozens of fighters from Russia who tried to sneak in with assault rifles and rocket-propelled grenades.

"There are grounds to believe that Russian terrorists are being sent onto Ukrainian territory, organised and financed under the direct control of the Kremlin and Russian special services," Ukraine's foreign ministry said, according to a McClatchy report.

"In fact, we are dealing with undisguised aggression against Ukraine from Russia, the Russian export of terrorism on the territory of our country."

The New York Times reported several of the rebel fighters wounded in the army's assault to free Donetsk airport were Russians, including Chechen mercenaries.

"We received an invitation to help our brothers," a Chechen fighter from Grozny who had fought in the Chechen War said, according to the report.

A Vice News video had got rebel fighters as saying: "We are volunteers, Chechens, Afghans and Muslims who have come to protect Russia, to protect Russians, to protect the interests of this country."

Pro-Russian separatists said they suffered heavy casualties in the Donetsk fighting.

"From our side, there are more than 50 (dead)," the prime minister of the rebels' self-styled Donetsk People's Republic, Alexander Borodai, told Reuters.

Unconfirmed reports have said more than 200 rebel fighters are unaccounted for after the airport showdown with Ukrainian army.

Earlier, in a sign that Kiev was toughening its stance against eastern separatism, newly elected President Petro Poroshenko put his weight behind the counter attack on rebels, saying military offensives against the "terrorists" should be swift and more effective.

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

The president also ruled out dialogue with them, saying no one holds talks with terrorists. "They want to preserve a bandit state which is held in place by force of arms ... These are simply bandits. Nobody in any civilized state will hold negotiations with terrorists."