Friedrich Merz, the unpopular and increasingly embattled German chancellor, vowed on Sunday evening that he would remain in the job, after his party performed poorly in two state elections in eastern Germany.

Mr. Merz’s center-right Christian Democrats, long the nation’s dominant conservative party, limped to their worst postwar showing in a state election, in the lightly populated coastal state of Mecklenburg-West Pomerania. In Berlin, the capital, they appeared on the brink of losing power after a surprisin