DONETSK, Ukraine -- Pro-Russia separatists and government forces battled at Donetsk airport in eastern Ukraine, claiming 40 lives, authorities said Tuesday, in what appears to be the deadliest outbreak of violence in the city.
Two of the fatalities are civilians.
An additional 31 people have been injured, including four civilians, according to the website of the Donetsk mayor, Alexander Lukyanchenko.
Donetsk International Airport was closed Tuesday following continuing clashes overnight.
A spokeswoman for the separatist self-declared "Donetsk People's Republic" said earlier Tuesday that 35 separatists had been killed and about 60 injured in Monday's fighting.
She said separatist militants control part of the Donetsk airport territory, and claimed that this means they control the airport. She conceded the Ukrainian national guard members were also on the airport's territory.
The Ukrainian authorities also claim they have control of the airport.
A team at a morgue in Donetsk saw a large pile of separatist militant bodies, many of which had been torn apart by shrapnel and explosions.
Doctors there said 31 bodies had been brought in with different types of injuries, from bullet wounds to those caused by heavy weapons and explosions.
Doctors also said some locals had arrived during the morning to identify and collect their relatives from among the dead.
Government air and ground forces attacked the pro-Russia militants after they seized a terminal at the airport early Monday.
Although the gunfire appeared to have halted by Tuesday morning, the airport is not expected to reopen for the moment.
A statement posted on the official website of the city's mayor advised residents to stay in their homes.
The country's anti-terror office spokesman, Vladislav Seleznev, said authorities have control of the airport as of Monday.
The preliminary evaluation is that the airport suffered minor damage on Monday, he said.
Experts are working to establish whether all the navigation and other systems are working, he said. In any case, it is not judged safe for airplanes to fly because the separatists have weapons capable of shooting at aircraft and seem willing to use them.
Monday's fighting marked the worst violence that this key population center in eastern Ukraine has seen since the start of the crisis. It erupted hours after newly elected Ukrainian President Petro Poroshenko said he'd potentially like to negotiate a way out of the crisis.
Poroshenko, a candy tycoon known as the "Chocolate King," is also a seasoned politician known for his pro-European Union views.
At a news conference in Kiev, he reiterated that European integration would be his priority. He added that in Sunday's vote, the President and the whole of Ukraine had changed.
Poroshenko also said Russia needed to participate in bringing peace to eastern Ukraine.
Separatist unrest over recent weeks has centered in the country's Donetsk and Luhansk regions.
Authorities canceled all flights after separatists stormed and seized Donetsk's airport terminal early Monday, according to the national news agency of Ukraine, Ukrinform. The separatists ignored a government ultimatum to vacate the premises, Ukrinform reported.
After a Ukrainian military plane "made a preliminary shot," paratroopers landed and began clearing the airport, Ukrinform reported. In the fighting, a separatist anti-aircraft gun was destroyed, the news agency said.
Though the Ukrainian government said it was taking control, reporters who witnessed the action saw separatist reinforcements moving toward the airport in trucks.
Both sides later claimed they held the airport.
Government officials had been optimistic that flights would resume by 9 a.m. (midnight MDT) Tuesday, but given the situation, it remains unclear when the airport will reopen.
Seleznev warned in a Facebook post Tuesday that if the rebels do not surrender, "terrorist" targets in Donetsk will be hit by "special high-precision weapons."
Ukraine's acting Interior Minister Arsen Avakov posted on his Facebook page Tuesday that an airstrike had destroyed a training camp in Yasenakh, in the Luhansk region.
Russian Foreign Minister Sergey Lavrov said Monday that Moscow would respect Ukrainians' choice in Sunday's election.
But, he added, Russia hopes that the new president will put an end to all "extremist activities" in eastern Ukraine and end its "anti-terrorist" operation in the eastern regions.
President Barack Obama congratulated Ukrainians for casting their ballots Sunday and criticized Russia-backed separatists, whom he accused of trying to block voting.
German Chancellor Angela Merkel, in a phone call with Poroshenko, hailed the vote as "a clear commitment of the Ukrainian people to unity and democracy as well as a peaceful solution to the current conflict," Merkel's spokesman said in a statement.
She said Germany would continue to support Ukraine on its democratic path, the spokesman said, adding that the two leaders agreed on the need to pursue internal reconciliation through national dialogue and constitutional reform.
At a news conference Monday, OSCE Parliamentary President Joao Soares said the presidential election was fair and represented the will of the Ukrainian people, despite major problems in Donetsk and Luhansk.