A Ukrainian special forces officer was killed in an operation launched by the government to reclaim a police station in the city.
Twenty men dressed in camouflage had commandeered the station Saturday.
Avakov said an unspecified number of activists had been wounded in the firefight.
"It is managed by Anti-terrorist Center of the Security Service of Ukraine," Avakov said of the operation on Facebook. "All the law enforcement agencies of the country are participating. Godspeed!"
"Tell all civilians to leave the center of town -- don't leave your apartment, or go to the window," he added.
CNN, though, said its reporters on the ground in Slovyansk didn't observe a large Ukrainian forces presence in the city, nor a confrontation with the activists.
Meanwhile, one other person died and four were injured in a gunfight at a checkpoint allegedly set up by pro-Russian activists along the road between Slovyansk and Donetsk.
[Wall Street Journal]