The unidentified man is calm, has not made any demands and is in regular contact with police via the telephones of the hostages, regional police chief Oleg Bekh told 112 news channel as Reuters reported.
Television footage showed police and parked police cars outside a two story white-and-yellow building in the northeastern city. The area has been closed off to traffic.
"We are trying to do everything to maintain communication with him and to do everything that is necessary to ensure the people are released," Bekh said.
The man in the post office was concerned about the recent prisoner exchange between the Ukrainian authorities and pro-Russian separatists and thought more prisoners should have been released, Bekh said, adding police did not know what he wanted.
Ukraine and the separatists swapped hundreds of prisoners on Wednesday in the biggest such exchange since the outbreak of a conflict in the eastern Donbass region that has killed more than 10,000 people.