(Adds seizing of another building, blocking of tanks)
DONETSK, Ukraine, April 15 (Reuters) - Pro-Russian separatists on Tuesday pulled out of one building they had occupied in an eastern Ukraine town but then rebels seized another in the same town, officials said.
Police first said separatists had voluntarily surrendered the police headquarters in Kramatorsk which was taken by armed militants on Saturday.
"They left of their own accord," Igor Dyomin, a spokesman for the Donetsk region police, told Reuters, though another version issued by police later said they quit the building as a result of negotiations.
But later on Tuesday a state security service (SBU) spokeswoman said rebels had occupied the local SBU offices in the same town. She gave no details.
Separatists, who the Kiev authorities say are inspired and organised by Russia, have been seizing buildings in Ukraine's border areas with Russia as counter action to the ousting of Moscow-backed President Viktor Yanukovich late last month.
The rebels, who have taken control of buildings in 10 localities in eastern Ukraine, have targeted police stations and SBU offices since they offer an easy supply of weapons.
Ukraine's authorities have announced a major "anti-terrorist operation" to quell the wave of separatist unrest though the crackdown has not been visible and government forces have not shown any readiness to storm occupied buildings.
In a separate incident in the Pershotravny region, about 100 pro-Russian separatists blocked the movement of a military unit, demanding they give up their arms, a local leader, Dmytro Chernytsa, said. He did not say how the unit had been blocked.
The activists drove off when two Ukrainian helicopters appeared, he said. (Reporting by Lina Kushch and Pavel Polityuk; Writing by Richard Balmforth; Editing by Louise Ireland)