(Fixes typo in first parahraph)
* Ukraine says separatists using heavy weapons, pilots killed
* Putin spokesman says "punitive operation" destroys deal
* Reuters reporters say military helicopter opened fire
* Four dead in Odessa disturbances
By Maria Tsvetkova
SLAVIANSK, Ukraine, May 2 (Reuters) - Pro-Russian rebels shot down two Ukrainian helicopters trying to retake separatist-held Slaviansk in the country's east on Friday and four people were killed as fighting broke out on the streets of Odessa on the Black Sea.
Separatists said Ukrainian forces killed three of their fighters and two civilians when they moved in on Slaviansk in the early hours in what Moscow called a "criminal" assault.
Kiev said two helicopter crew had died and seven servicemen had been wounded in the operation.
On the other side of Ukraine, police said three people were shot dead and in 15 others were wounded in clashes between people backing Kiev and pro-Russian activists in largely Russian-speaking Odessa. Another man was killed and a building was set on fire as the fighting continued into the evening.
The southern Black Sea port lies close to Crimea, which was annexed by Moscow in March following the overthrow of Ukraine's pro-Moscow president by protesters angered by his decision to scrap a trade deal with Europe.
President Vladimir Putin's spokesman said Ukrainian forces had fired on civilians from the air in Slaviansk in a "punitive operation" that destroyed an international peace plan. Moscow has tens of thousands of troops massed on the border and claims the right to invade if needed to protect Russian speakers.
The Western-backed government in Kiev said the use of missiles to bring down its helicopters showed Russian forces were in the town. Moscow denies its troops are on the ground.
Ukraine's acting president also said Russian "armed saboteurs" had tried to enter the country overnight, but were pushed back by Ukrainian border troops. Russia's Security Service said the report was untrue.
Kiev said Moscow was backing groups in eastern Ukraine who were "putting civilians in danger, seizing hostages and creating an atmosphere of terror and violence".
Reuters journalists in Slaviansk, the most heavily fortified bastion of pro-Russian separatists in eastern Ukraine, heard shooting and saw one helicopter opening fire before dawn. Later in the day, the city was largely quiet, with shops shut and armed separatists in control of the streets.
Advancing Ukrainian forces in armoured vehicles took up positions in the suburbs, but rebels still controlled most of the town of 130,000.
Acting President Oleksander Turchinov said the operation had been complicated by the rebels' use of human shields and had not progressed as quickly as had been hoped.
SOUND OF CANNON
The growing chaos is overshadowing a presidential election the pro-Western leadership in Kiev is planning for May 25. The rebels are planning a vote on May 11 to seek a mandate to break with Kiev, like one held in Crimea before Moscow took it over.
The United States and Europe have imposed sanctions on individuals over the Ukraine crisis but they have had limited impact. U.S. President Barack Obama said the next step would be sanctions on sectors of the Russian economy and they would be imposed if Moscow impeded the Ukrainian presidential poll.
German Chancellor Angela Merkel, visiting Washington, told a joint news conference with Obama that the elections on May 25 were critical and sectoral sanctions were ready.
The energy and banking sectors are likely targets.
On the square outside city hall in Slaviansk, about 100 people gathered on Friday and said they were appealing to Putin to send troops to help them.
Businesswoman Tamara Voshchanaya said: "What can you think when the sound of cannon makes you jump out of bed, when helicopters are flying over and shooting at our guys?
On the town's southern outskirts, eight Ukrainian armoured personnel carriers cut off the road but faced a cordon of local residents shouting at them to go home. Some rebels erected barricades of trees.
Putin's popularity has soared with the seizure of Crimea and talk of restoring Moscow's former empire. This week he restored the Soviet-era tradition of holding a May Day parade on Red Square, where marchers carried banners hailing the acquisition of Ukrainian territory.
U.S. Defense Secretary Chuck Hagel said Russia's actions in Ukraine had shattered the myth of European security in the post-Cold War era and said NATO allies had increased the danger by failing to meet their defence spending pledges.
The European Union said it was watching events in eastern Ukraine with growing concern. But Kiev is not a member of NATO and Western leaders have made clear they will not fight to defend Ukraine.
The Ukrainian Defence Ministry said two Mi-24 attack helicopters had been shot down by shoulder-launched missiles while on patrol overnight around Slaviansk. Two airmen were killed and others wounded.
Other Ukrainian officials and the separatist leader in Slaviansk said earlier that one airman was taken prisoner.
A third helicopter, an Mi-8 transport aircraft, was also hit and a serviceman wounded, the Defence Ministry said. The SBU security service said this helicopter was carrying medics.
Ukrainian officials said their troops overran rebel checkpoints and Slaviansk was now "tightly encircled".
Putin's spokesman heaped blame on the Ukrainian government, which took power two months ago after pro-Western protests forced president Viktor Yanukovich to flee to Russia.
Noting that Putin had warned before that any "punitive operation" would be a "criminal act", Dmitry Peskov told Russian news agencies that this had now happened in Slaviansk.
"While Russia is making efforts to de-escalate and settle the conflict, the Kiev regime has turned to firing on civilian towns with military aircraft and has begun a punitive operation, effectively destroying the last hope of survival for the Geneva accord," he said, referring to a deal on April 17 signed by Russia, Ukraine, the United States and the European Union.
Under that agreement, separatists were supposed to lay down their arms and vacate the public buildings they have seized in about a dozen towns they have seized across the Russian-speaking east. Since then, however, they have tightened their grip.
Ukraine's Interior Ministry said it persuaded separatists to leave two buildings in the city of Luhansk on Friday.
The SBU said the deadly use by the separatists of shoulder-launched anti-aircraft missiles was evidence that "trained, highly qualified foreign military specialists" were operating in the area "and not local civilians, as the Russian government says, armed only with guns taken from hunting stores".
On Facebook, Interior Minister Arsen Avakov said his message to the separatists was simple: "Free the hostages, lay down weapons, vacate administrative buildings and get municipal infrastructure back to normal."
The rebels said they had the upper hand.
"They wanted to carry out some small-scale tactical operations just to scare the people," said a militant at a checkpoint. "But so far things have not worked out the way they wanted." (Additional reporting by Natalia Zinets and Elizabeth Piper in Kiev and Matthew Robinson in Donetsk; writing by Alastair Macdonald and Philippa Fletcher; editing by Peter Graff and Giles Elgood)