CHISINAU, Moldova — On Friday, Natalia Gavrilita was a director at an aid group in London. On Saturday, she was unexpectedly named minister of finance in her native Moldova. On Monday, she flew home to start her new job.

There’s just one hitch: Her predecessor won’t leave, and the police won’t let her enter her office.

Such are the competing realities in Moldova, a small former Soviet state in southeast Europe, where two of the country’s three largest parties formed a new coalition government on Saturday in order to oust the third from power. But the latter, the Democratic Party of Moldova, has refused to leave office — leaving the country with two claimants to every ministry.

“We have two parallel stories,” said Dumitru Alaiba, a lawmaker from one of the two parties forming the would-be new government. “We have a former prime minister who is refusing to leave.”

The chaos has been compounded by the Constitutional Court, staffed in part by longtime associates of the Democratic Party leader, the oligarch Vladimir Plahotniuc.