The deaths came as pro-Russian protesters clashed with Ukrainian government supporters in the city.Officials said some people were overwhelmed by smoke and others died after they jumped from the building.Earlier President Oleksandr Turchynov said many separatists had been killed in a government offensive in Sloviansk.Activists have seized scores of government buildings and detained observers in eastern Ukraine.The fire broke out in Odessa's Trade Unions House, the regional office of Ukraine's interior ministry said. It did not give details of how the blaze started.The exact sequence of events is still unclear, but reports suggest the separatists had barricaded themselves inside the building and both sides were throwing petrol bombs.The interior ministry gave a toll of at least 31 dead, revising down an earlier tally of 38 killed.Ukrainian Deputy Foreign Minister Danylo Lubkivsky told the BBC he regretted the loss of life but insisted Russia was behind the violence."The situation remains under control. But the security situation is threatened by Russian special agents," he said."That's why we are requesting and demanding Russian authorities to stop their efforts that can undermine regional security and stability."Russia's foreign ministry said Moscow was "outraged" by events in Odessa and denounced Kiev's "irresponsibility".The US called the violence "unacceptable" and urged both Ukraine and Russia to restore order."The violence and mayhem that led to so many senseless deaths and injuries is unacceptable," the state department said in a statement.GunfireEarlier, four people were killed in clashes between the pro-Russian and pro-Kiev protesters in the city - the first such eruption of violence in the south after weeks of mounting unrest in Ukraine's east.BBC Map of Odessa and Trade Unions HouseIt followed a rally by Ukrainian football fans, reports say.The BBC's David Stern in Kiev says the death toll in Odessa is the highest since violence broke out between pro-EU protesters and police in the capital in February.The Black Sea city is ethnically mixed with a large number of Russian speakers, our correspondent says.Meanwhile the latest reports from rebel-controlled Sloviansk in the east say intense gunfire has broken out in the centre of the city.During the day government forces took over pro-Russian checkpoints outside the city.Separatists shot down two Ukrainian army helicopters, killing a pilot and another serviceman.'Catastrophic consequences'The West continues to accuse Moscow of provoking the unrest in eastern Ukraine, something Russia denies.US President Barack Obama, at a meeting with German Chancellor Angela Merkel at the White House, warned of further sanctions against Russia if it did not "change course".He said the idea that the unrest was caused by a "spontaneous uprising" was "belied" by the militants' use of missiles.The UN Security Council met earlier on Friday for an emergency session at Russia's request.Moscow's ambassador warned of "catastrophic consequences" if Kiev's military operation in eastern Ukraine continued, while the US called it "proportionate and reasonable".Eastern Ukraine has a large Russian-speaking population. It was a stronghold for President Viktor Yanukovych before he was overthrown by pro-Western protesters in February.Russia then annexed the Crimean peninsula - part of Ukraine but with a Russian-speaking majority - in a move that provoked international outrage.The crisis has plunged East-West relations to their lowest point since the Cold War ended in the early 1990s.(BBC)BakuDaily.Az