A revised Ukrainian government statement said the fire broke out in a trade union building, and that 31 bodies were found at the scene - seven fewer than police first reported. Most of the victims were apparently members of pro-Russian groups. The Russian news agency RIA Novosti said about 50 other people were injured, including 10 police officers.
Odessa, a key Black Sea port, had largely escaped the violence gripping large parts of eastern Ukraine.
Earlier Friday, Ukrainian government forces launched the first major assault on the rebel-held eastern city of Slovyansk. Pro-Russian separatists brought down two Ukrainian military helicopters involved in the operation.
Eastern Ukraine has been a focus of concern in Western capitals since Moscow annexed mainly Russian Crimea from Ukraine in March. Clashes have also broken out in largely Russian-speaking Odessa, not far from Crimea, but they had never involved deaths before.
Police said at least three people were shot dead and 15 others were wounded in running battles between people backing Kyiv and pro-Russian activists in the town. The fighting continued into the evening.
In the east, separatists said Ukrainian forces killed three of their fighters and two civilians when they moved in on Slovyansk in the early hours on Friday in what Moscow called a ``criminal'' assault.
Kyiv said two helicopter crew members had died and seven servicemen had been wounded in the operation, which it admitted had not achieved much.
Western media said Ukrainian forces had seized rebel checkpoints on the outskirts of the city, but have not advanced toward its heavily fortified center.
President Vladimir Putin's spokesman said Ukrainian forces had fired on civilians from the air in Slovyansk 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.
UN Security Council
In New York, Western powers and Russia used an emergency session of the United Nations Security Council to accuse each other of failing to take appropriate steps to de-escalate the crisis.
British Ambassador Mark Lyall Grant said "the scale of Russian hypocrisy is breathtaking."
For his part, Russian Ambassador Vitaly Churkin accused the West of applying double standards in the crisis by condoning the current Ukrainian offensive, after urging then-Ukrainian president Viktor Yanukovych not to deploy troops when his government in Kyiv was under siege earlier this year.
And in Washington on Friday, U.S. President Barack Obama warned that If Moscow continues fueling unrest in Ukraine, Putin and others in his leadership circle will face increasingly broad sanctions.
During a joint news conference at the White House Rose Garden, Obama and German Chancellor Angela Merkel said they want to see a diplomatic resolution to the crisis.
Otherwise, Obama and Merkel warned Russia that if it further destabilizes Ukraine or interferes in Ukraine's May 25 presidential elections, it will face more sanctions.
Moscow presence questioned
Earlier Friday, the Western-backed government in Kyiv said the use of missiles that brought down its helicopters was evidence that Russian forces were in the town. Moscow denies that its troops are on the ground.
Ukraine's Turchynov said Russian ``armed saboteurs'' had tried to cross into the country overnight, but were pushed back by Ukrainian border troops. He gave no further details.
Russia's Security Service said his report was untrue.
Turchynov said the military operation had been complicated by the rebels' use of human shields and had not progressed as quickly as had been hoped.
By early afternoon Friday, military operations in and around Slovyansk appeared to have ceased, leaving the region in a state of tension and Ukrainian and separatist forces facing off near a strategic bridge that was under government control. The Ukrainians did not seem eager to engage the militants, limiting their activities to tightening a cordon around the city of 130,000, the New York Times reported.
The growing chaos is overshadowing a presidential election the pro-Western leadership in Kyiv is planning for May 25. The rebels are planning a vote on May 11 to seek a mandate to break with Kyiv, like one held in Crimea before Moscow took it over.
The European Union said it was watching events in eastern Ukraine with growing concern. But Kyiv is not a member of NATO and Western leaders have made clear they will not fight to defend Ukraine.
U.S. Defense Secretary Chuck Hagel said NATO's European members needed to increase their defense spending in light of Russia's action in Ukraine.
Hagel said one of the biggest obstacles to investment in defense was the sense that the prospect of conflict among nations had dissipated with the end of the Cold War.
"Russia's actions in Ukraine shatter that myth and usher in bracing new realities," he said, speaking about the future of the NATO alliance at the Wilson Center in Washington on Friday.
"Over the long term, we should expect Russia to test our alliance's purpose, stamina, and commitment," Hagel said.
Earlier Friday, the Ukrainian Defense Ministry said in a statement that two Mi-24 attack helicopters had been shot down by shoulder-launched anti-aircraft missiles while on patrol overnight around Slovyansk.
A third helicopter, an Mi-8 transport aircraft, was also hit and a serviceman wounded, the Defense Ministry said. Ukraine's Secret Security Service said this helicopter was carrying medics.
Ukrainian officials said their troops overran rebel checkpoints and Slovyansk was now "tightly encircled."
Some information in this report was contributed by Reuters, AP.