Ukrainian paratroopers and pro-Russian rebels were battling Tuesday for control of Donetsk airport after a day of intense firefights that marked a sharp escalation of the conflict in the east of the country.
Local health officials confirmed there had been fatalities from Monday's gunbattles but did not give a precise toll.
A series of explosions and gunfire were heard early Tuesday from the direction of the airport and an AFP correspondent reported seeing body parts and blood splattered on the road near bullet-riddled truck.
Combat jets and helicopter gunships attacked the airport terminal in the eastern industrial hub on Monday after it was seized by scores of separatist gunmen waging an insurgency against Kiev's rule.
"It is not clear who is in control of the airport," airport spokesman Dmitry Kosinov told AFP on Tuesday.
The fighting flared on very day that billionaire oligarch Petro Poroshenko was formally declared the winner of Sunday's presidential election with 54 percent of the vote.
Poroshenko pledged to work to restore stability in Ukraine after months of turmoil but vowed he would not negotiate with "terrorists" he said wanted to turn the country into another Somalia.
Monday's air 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.
Scores of gunmen had stormed the airport in an apparent show of defiance against Poroshenko, underscoring the daunting challenges ahead if he is to prevent a Balkans-style war erupting on Europe's eastern doorstep.
Ukraine's election chief on Monday confirmed the billionaire chocolate baron's victory, saying his 41-point lead over closest rival, former prime minister Yulia Tymoshenko, was unassailable with only a tenth of the ballots left to count.
Even before the results, the 48-year-old Poroshenko had moved swiftly to stamp his authority as Ukraine's new leader, vowing to rebuild relations with Russia while steering the country on a westward path.
He said Ukraine would press on with its offensive against insurgents who control about a dozen cities and towns but said he wanted it to be "more efficient".
But he refused to open dialogue with the rebels until they laid down their arms.
"Their goal is to turn Donbass (east Ukraine) into Somalia. I will not let anyone do this to our state."
Sunday's vote was seen as the most important since Ukraine's independence in 1991 as it fights to stay united and avert economic collapse after years of Soviet-era mismanagement and rampant corruption.
But the insurgency, which has already cost at least 150 lives, thwarted polling in much of the east and rebels have defiantly refused to recognise the result.
Russia, threatened with more Western sanctions if it meddled further in Ukraine after its seizure of Crimea in March, said it was willing to work with the new leader.
"We are ready for pragmatic dialogue, on an equal footing, based on respect for all agreements, in particular in the commercial, economic and gas spheres," Foreign Minister Sergei Lavrov said. "We respect the result of the choice of the Ukrainian people."
Poroshenko also said he was ready to "engage" with the Russian leadership and was optimistic a meeting could be arranged with President Vladimir Putin soon.
Donetsk separatist leader Denis Pushilin said talks with Kiev were only possible if Russia mediated and there was a prisoner swap and a withdrawal of Ukrainian troops.
Analysts see Poroshenko's emphatic victory as a first step in trying to restore stability but, said Holger Schmieding of Berenberg Bank: "That does not end the conflict in Ukraine."
While turnout was strong across the capital Kiev and the more pro-European west on Sunday, voting was largely blocked in Donetsk and Lugansk where rebels have declared their own independent states.
Observers with the Organisation for Cooperation and Security in Europe said the election "largely upheld democratic commitments" and provided the new leader with legitimacy.
US President Barack Obama praised "courageous Ukrainians" for voting in the face of the militant threat and said Washington looked forward to working with the new president.
The ballot was called after pro-Russian president Viktor Yanukovych -- his corruption-stained regime long a source of discontent -- was ousted in February in the bloody climax of months of protests sparked by his rejection of closer EU ties.
Putin responded by seizing Crimea and threatening to invade the rest of Ukraine to "protect" the country's ethnic Russian community.
But Russia said last week it had started withdrawing from Ukraine's border around 40,000 soldiers whose presence had raised deep Western suspicions.