The Ukrainian city of Donetsk is in turmoil a day after government forces used fighter jets to stop pro-Russia separatists from taking over the airport.
The mayor of the eastern city said 40 people were killed and went on television to urge residents to stay at home.
The city of one million was engulfed by fighting yesterday when rebels moved to seize the airport, Ukraine's second largest.
They were repelled by government forces using combat jets and helicopter gunships, and officials shut down Donetsk airport and nearby streets to traffic amid the fighting.
Mayor Oleksandr Lukyanchenko was quoted by the local news portal Ostrovas saying that 40 people, including two civilians, were killed in the fighting.
The bodies of about 30 insurgents were taken to a hospital morgue in Donetsk, said Leonid Baranov of the separatist Donetsk People's Republic, who was at the Kalinin morgue.
The fighters had been wounded and were being transported to a hospital in a truck when it was targeted by government forces, Mr Baranov said.
He said other fighters were also killed but their bodies had not been recovered because they were in areas under government control. He said hundreds were wounded in the fighting.
The battles came as billionaire chocolate magnate Petro Poroshenko claimed victory in Sunday's presidential vote, which authorities in the capital of Kiev had hoped would unify the deeply divided nation.
Mr Poroshenko, who is yet to be sworn in, has vowed to negotiate a peaceful end to the insurgency in the east, but has called the separatists "Somali pirates" and promised he would stop them from sowing more chaos.
Early today, unidentified men stormed Donetsk's main ice hockey arena and set it ablaze, according to the mayor's office. The arena, owned by a local Ukrainian politician, was to host the 2015 world championships.
By this morning, the airport was under full government control, Ukraine's acting interior minister Arsen Avakov said, adding that dozens of insurgents might have been killed in the fighting but government forces did not suffer any casualties.
In the neighbouring Luhansk region, which like Donetsk has declared independence from the central government, the Ukrainian Border Guards Service said its officers fought a gun battle with a group of gunmen who were trying to break through the border from Russia.
It said one intruder was wounded and the border guards seized several vehicles loaded with Kalashnikov assault rifles, grenade launchers and explosives.
The interim government in Kiev has pledged to press ahead with the operation against insurgents, which has angered local residents, many of whom see the government as nationalists bent on repressing Russian speakers in the east.
Speaking at a televised government session, Vitaly Yarema, a deputy prime minister, said the "anti-terrorist operation" in eastern Ukraine will go on "until all the militants are annihilated".
In Moscow, Russian foreign minister Sergey Lavrov voiced strong concern about the interim authorities' decision to intensify the military operation in the east and called for an immediate end to fighting.
Mr Poroshenko, known for his pragmatism, supports building strong ties with Europe but has stressed the importance of mending relations with Moscow. Upon claiming victory, he said his first step as president would be to visit the troubled east.
He said he hoped Russia would support his efforts to bring stability and that he wanted to hold talks with Moscow.
Mr Lavrov welcomed his promise to negotiate with people in the east and said Moscow was ready for direct talks with Mr Poroshenko. He also said Russia does not want the United States and the European Union as mediators.
But Ukraine's acting prime minister Arseniy Yatsenyuk said Ukraine has no intention of talking to Russia directly.
"The government's stance is unchanged: bilateral talks without the presence of the United States and the European Union do not seem possible under current conditions," he said.