Reports say sporadic fighting is continuing on the outskirts of the eastern Ukrainian city of Donetsk, a day after heavy clashes in which dozens of pro-Russian separatists were reported killed.
Ukrainian local and national authorities also report that security forces have regained control of the airport, which was occupied by gunmen on May 26.
The separatists said at least 30 and possibly up to 100 fighters were killed during nearly 24 hours of fighting that followed the airport seizure.
The mayor of Donetsk, Oleksandr Lukyanchenko, said the death toll from the fighting stood at 40, including two civilians. He did not specify whether the remaining 38 dead were rebels or government troops.
Pavel Gubarev, the self-proclaimed "people's governor" of Donetsk, said government forces opened fire on a truck carrying wounded fighters from the airport to a hospital, killing 35. He said another 15 fighters were injured.
It was not immediately clear whether the reports referred to the same incident.
Interior Minister Arsen Avakov said the rebels had suffered heavy losses but gave no figures. He said no government troops were killed.
WATCH: The bodies of pro-Russian separatists were delivered to a morgue in the eastern Ukrainian city of Donetsk on May 27 (NOTE: GRAPHIC CONTENT).
The fighting -- in which government forces used combat jets and helicopter gunships -- began after the separatists seized the Donetsk airport on May 26 and continued into the following day.
It was the first time the fighting has spread to the city of Donetsk since the unrest in eastern Ukraine began some two months ago.
Avakov said on May 27 that government forces now controlled the airport, but an airport spokesman, Dmytro Kosinov, told AFP that it was not clear who was in control.
First Deputy Prime Minister Vitaliy Yarema said that the "antiterrorist operation" will continue "until not a single terrorist remains on the territory of Ukraine."
Media reports said a group of separatists attacked a hockey arena in Donetsk on May 27, setting fire to part of the building. There were no injuries in that incident.
Meanwhile, Ukraine's Border Guards Service said border guards in the neighboring Luhansk region opened fire overnight on a convoy of vehicles carrying rebels that had allegedly crossed over from Russia.
At least one rebel was killed in the firefight. The border guards also said they seized several vehicles allegedly carrying weapons.
WATCH: Woman killed by shrapnel at Donetsk railway station.
Petro Poroshenko, the victor in Ukraine's May 25 presidential election, has vowed to open a dialogue with residents of Ukraine's eastern regions but rejected talks with "terrorists."
"The antiterrorist operation cannot and should not last two or three months. It should and will last hours," Poroshenko added.
He said he hoped Russia would help bring stability to the east and that he wanted to hold talks with Moscow to resolve the crisis, but Russian Foreign Minister Sergei Lavrov on May 27 said a visit to Moscow by Poroshenko was "not being considered."
Lavrov on May 27 called for an immediate end to the Ukrainian military operation in eastern Ukraine and violence "on all sides."
Russian President Vladimir Putin called for an immediate end to what he called the Ukrainian government's "punitive" military operation in the east.
With reporting by AP, Reuters, UNIAN, and RFE/RL's Ukrainian Service