The city of 1 million was engulfed by fighting Monday when rebels moved to seize the airport, Ukraine's second largest. They were repelled by government forces using combat jets and helicopter gunships. Associated Press journalists witnessed intensive gun fire throughout the day and into the night. Plumes of black smoke rose into the air and officials shut down Donetsk airport and nearby streets to traffic amid the fighting.
Donetsk mayor Oleksandr Lukyanchenko was quoted by the local news portal Ostrovas saying that 40 people, including two civilians, were killed in Monday's fighting.
The bodies of about 30 insurgents showed up at a hospital in Donetsk on Tuesday, according to a rebel fighter who wouldn't give his name because of security concerns. Speaking outside the hospital, he said the truck carrying the bodies was still parked nearby, waiting for explosives experts to check it for any unexploded ordnance.
There was no immediate confirmation yet from the hospital about the bodies.
The battles came as billionaire candy 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. Poroshenko, who is yet to be sworn in, has vowed to negotiate a peaceful end to an insurgency in the east but also has called the separatists "Somali pirates" and promised he would stop them from sowing more chaos.
Early Tuesday, 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 lawmaker, was to host the 2015 world championships.
By Tuesday morning, the Donetsk airport was under full government control, Ukraine's acting Interior Minister Arsen Avakov said, adding that dozens of insurgents may have been killed in the fighting but government forces did not suffer any casualties.
In the neighboring Luhansk region, which like Donetsk has declared independence from the central government, Ukrainian Border Guards Service said its officers fought a gunbattle 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, rocket 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 on Tuesday, 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 a strong concern Tuesday about the interim authorities' decision to intensify the military operation in the east and called for an immediate end to fighting.
Poroshenko, known for his pragmatism, supports building strong ties with Europe but also 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.
Lavrov welcomed Poroshenko's promise to negotiate with people in the east and said Moscow was ready for direct talks with Poroshenko. He also pointedly said Russia doesn't 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.
Moscow has denied accusations by the authorities in Kiev and the West that it has fomented the insurgency in eastern Ukraine. Russian President Vladimir Putin annexed the Ukrainian Black Sea peninsula of Crimea in March but has stonewalled the eastern insurgents' appeal to join Russia.
Putin has also welcomed the Ukrainian presidential election in an apparent bid to de-escalate tensions with the West, which hit his entourage with sanctions for the annexation of Crimea.
Russia has kept pushing for Ukraine to decentralize its government, which would give more power to the regions, including those in the east, and allow Moscow to keep those areas in its sphere of influence.
Nataliya Vasilyeva and Laura Mills in Kiev, Ukraine and Vladimir Isachenkov in Moscow contributed to this report.
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