BERLIN — Voters in Germany’s most populous state strengthened a center-left regional government which Chancellor Angela Merkel’s conservatives sought to portray as irresponsibly spendthrift, and inflicted an embarrassingly heavy defeat Sunday on the German leader’s party, projections showed.

The center-left Social Democrats and Greens — Germany’s main opposition parties — won combined support of about 51 percent in the election in North Rhine-Westphalia state, according to ARD television based on exit polls and early counting.

That would be enough to give them a majority in the state legislature, which they narrowly missed in the last regional election two years ago.

Support for Merkel’s Christian Democrats was seen dropping to 26 percent from more than 34 percent, their worst showing in the state since World War II. But the pro-market Free Democrats, Merkel’s struggling partners in the national government, performed respectably — polling more than 8 percent to buck speculation that they might fail to win seats.

The incumbent government of popular governor Hannelore Kraft had been favored to win, particularly after a much-criticized and sometimes gaffe-prone campaign by conservative challenger Norbert Roettgen, Merkel’s federal environment minister. The vote came as Germany starts looking toward national elections due late next year.

“This is a crashing defeat for Mrs. Merkel and her minister,” said Andrea Nahles, the Social Democrats’ general secretary.

“The defeat is bitter, it is clear and it really hurts,” a crestfallen Roettgen said minutes after the polls closed, announcing that he would give up the leadership of the Christian Democrats’ local branch.

“This is, above all, my personal defeat,” he said.