Ukraine's acting president said pro-Russia insurgents have suffered significant losses - including many killed and injured - after his government launched an offensive on the rebel-held city of Sloviansk on Friday.
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The Kremlin, meanwhile, said Kiev's offensive "destroyed" the two-week-old agreement on cooling Ukraine's crisis.
Pro-Russia separatists shot down two of the attack helicopters, killing their pilots, in a sharp escalation of the conflict.
The Ukrainian Security Service said one of the helicopters was shot down with a surface-to-air missile, which it said undercut Russia's claims that the city is under control of civilians who took up arms. It added that one pilot was captured alive by the separatists.
Russian President Vladimir Putin's spokesman said on Friday that Kiev had launched a "punitive operation" in south-east Ukraine, destroying the final hope of keeping alive an accord intended to defuse the Ukraine crisis, Russian news agencies reported.
They quoted spokesman Dmitry Peskov as saying Putin had sent a representative to the area for talks about freeing captured Organisation for Security and Cooperation in Europe observers but that the Kremlin had not been in contact with him since the operation began.
Russia denies involvement but has massed troops on the border and threatened to intervene to protect the Russian-speaking majority in eastern Ukraine from what it calls an illegitimate, Western-backed government in Kiev. Alarmed Western powers believe President Vladimir Putin is set on asserting Moscow's influence over its former Soviet neighbors.
Armed groups seeking union with Russia have seized a number of government buildings in towns in eastern Ukraine. The action in Slaviansk appeared to mark the heaviest military response by Kiev since it tightened a cordon around the city a week ago.
The militants in Sloviansk are holding a number of local people and seven foreign military observers, four of them German, from the European security agency the OSCE.
On his Facebook page, Interior Minister Arsen Avakov posted: "The goal of our anti-terrorist operation and, at the same time, our demands to the terrorists are simple: Free the hostages, lay down weapons, vacate administrative buildings and get municipal infrastructure back to normal."
He urged locals to stay indoors and said Ukrainian forces, from the Interior Ministry, National Guard and the armed forces, had orders not to fire on residential buildings.
Support for the separatist movement is patchier in eastern Ukraine than it was among the majority ethnic Russian population of Crimea, which Moscow seized and annexed in March. However, many are fearful of the new authorities in Kiev and have little faith in Ukraine after 23 years of post-Soviet independence marked by rampant corruption and poor living standards.
"Shells came into my garden," said one local man, Gennady. "They say that they have come to defend us. But who from?" he said of the Ukrainian forces. "Civilians must stop them."
Citing the situation in the east, acting Ukrainian President Oleksander Turchinov has signed a decree reinstating compulsory military service for men aged between 18 and 25.
The Kiev government, along with its Western allies, accuses Moscow of orchestrating the uprising. The United States and European Union have imposed sanctions in response to Russia's annexation of Crimea and involvement in eastern Ukraine.
Russia denies having any part in the rebellion, but has warned it reserves the right to intervene to protect ethnic Russians and has massed tens of thousands of troops on its western frontier with Ukraine.
Putin has described the break-up of the Soviet Union as a tragedy and overturned years of post-Cold War diplomacy in March by declaring Moscow's right to intervene in former Soviet republics to protect Russian speakers.
The U.S. and EU sanctions, while not hitting Russian industry directly, have hurt the economy by scaring investors into pulling out capital. The IMF cut its outlook for Russian economic growth this year to just 0.2 percent on Wednesday and said Russia was already "experiencing recession".
U.S. aluminum producer Alcoa said its Chief Executive Klaus Kleinfeld had cancelled plans to attend Putin's St. Petersburg International Economic Forum later this month.
Kiev ordered the expulsion of Russia's military attachי on Thursday, saying it had caught him "red-handed" receiving classified information from a colonel in Ukraine's armed forces on the country's cooperation with NATO.
A spokeswoman for Ukraine's security service, the SBU, said the attachי had been handed over to the Russian embassy and ordered to leave, although she was not sure if he had left yet.
NATO said on Thursday it was looking at ways to bring former Soviet state Georgia, which Russia invaded in 2008, "even closer" to the military alliance. Russian forces defend two breakaway Georgian regions, comprising a fifth of its territory.
Moscow strongly opposes Georgia joining NATO.
Last week, France and Germany assured Georgia that a deal bringing it closer to the EU would be sealed soon.
Romania, a formerly part of the Soviet bloc but now a NATO member, called on Thursday for the United States and the Western alliance to boost their military presence there.
Moscow mayor Sergei Sobyanin told Rossiya 24 TV that more than 100,000 people had marched through Red Square on Thursday, saying there was a "patriotic uplift" in Russia. Russian television also showed footage of a May Day parade in Crimea's capital, Simferopol.
The intervention in Ukraine has been enormously popular in Russia. One opinion poll on Wednesday showed 82 percent support for Putin, his highest rating since 2010.