In separatist-held Slaviansk, the self-declared mayor said he would discuss the release of detained military observers only if the European Union dropped sanctions against rebel leaders.
"The regional leadership does not control its police force," said Stanislav Rechynsky, an aide to Interior Minister Arsen Avakov, referring to events in Luhansk where separatists had earlier only occupied the local security services' building.
"The local police did nothing."
He added that the ministry had information that they would next try to take the local television centre.
Some protesters, who say they are not properly represented in Kiev by Ukraine's new pro-Western rulers, called on the police to handover their arms.
Turchynov demands police dismissals in east
Ukraine's acting president demanded the dismissal on Tuesday of police chiefs in the eastern cities of Donetsk and Luhansk, saying much of the police in the east of the country had proven incapable of fulfilling their duties.
The statement by Oleksander Turchynov followed the takeover by armed pro-Russian separatists of several state buildings in Luhansk on Tuesday, unopposed by police.
"The overwhelming majority of law enforcement bodies in the east are incapable of fulfilling their duty to defend our citizens," he said.
Opposition to sanctions
Ukraine's authorities are struggling to find a way to evict the separatists, who also took a small town hall in Pervomaisk in the Luhansk region on Tuesday.
Kiev launched an "anti-terrorist" operation in early April, but so far it has failed to yield many results.
Some separatists have begun to call the shots.
Vyacheslav Ponomaryov, the self-declared mayor of Slaviansk, told Interfax news agency that EU sanctions against two rebel leaders were "not conducive to dialogue" on releasing six military observers detained after being accused of harbouring a Ukrainian spy.
Read MoreWho are the separatist rebels destabilizing Ukraine?
The observers had travelled to eastern Ukraine under the auspices of the Organization for Security and Cooperation in Europe (OSCE), a democracy watchdog.
"If they fail to remove the sanctions, then we will block access for EU representatives, and they won't be able to get to us. I will remind my guests from the OSCE about this," he said.
Separatists in Donetsk, eastern Ukraine's second biggest city, have said they will hold a referendum on independence for the Donbass region on May 11.
That would undermine government efforts to hold a non-binding consultative referendum across Ukraine on May 25 or June 15, when the country votes for the president, to gauge appetite for the decentralisation of power.
Russia has denied suggestions that it is orchestrating events in eastern Ukraine and that it plans to invade eastern Ukraine, which is home to many Russian speakers, following its annexation of the Crimea peninsula.