More than 30 people have reportedly been killed in a fire at the labor-union building in the southern Ukrainian port city of Odesa.
It was unclear how the fire started. Some reports say Molotov cocktails had been thrown at the union headquarters building.
Those inside the building were said to be pro-Russian activists.
Some agencies quoted local police as saying the death toll was at least 38 and that more than half had died jumping from upper-floor windows to escape the fire.
Ukraine's UNIAN news agency reported the pro-Russian separatists were shooting from the roof of the building at supporters of the Kyiv government.
Reports said the second and fourth floors of the five-story building were engulfed in flames.
"The violence and mayhem that led to so many senseless deaths and injuries is unacceptable," U.S. State Department deputy spokeswoman Marie Harf said in a statement.
There had been clashes between the two groups in areas of Odesa since the afternoon, in which at least three people were reportedly killed and 50 injured.
Sporadic clashes between the two groups were reported from the afternoon into the evening.
Meanwhile, Ukraine says military operations against pro-Russian separatists in the east of the country continued at dawn on May 3.
Interior Minister Arsen Avakov said Ukrainian troops had taken control of a television town in Kramatorsk. "We are not stopping," Avakov wrote on his Facebook page.
On May 2, the Kyiv authorities had launched a military operation against pro-Russian separatists who seized control of government buildings in Slovyansk.
Russia, which has deployed an estimated 40,000 soldiers on its border with Ukraine, says Kyiv's use of military force "against its own people" in eastern Ukraine will lead to a "catastrophe."
Ukrainian Interior Minister Arsen Avakov said the goals of the offensive were to get pro-Russian separatist forces to "free the hostages, lay down their arms, and free administrative buildings, and restore the normal functioning of the town's administration."
He also described the pro-Russian separatist forces as professional mercenaries.
At least three people were killed in the battle for control of checkpoints on the outskirts of Slovyansk, including two Ukrainian pilots whose helicopters were shot down and at least one pro-Russian fighter.
A spokeswoman for separatist forces in Slovyansk told RFE/RL that more separatists had been killed but did not provide a number.
Based on reporting by AP, Reuters, UNIAN, ITAR-TASS, and Interfax