The upstart Alternative for Germany (AfD) party, a populist force that campaigned on an anti-migrant, anti-Merkel platform — and which drew support from the left as well as the right — scored big gains. It landed 24.4 percent of the vote in one of the three states that went to the ballot box, according to projections based on exit polls produced for the German public broadcaster ARD.

The outcome amounted to a blow to Merkel just as the chancellor is set to fight this week for a new accord between the European Union and Turkey on the refugee crisis. It would stop the illegal flow of migrants across the Aegean Sea, but also compel reluctant European nations, including Germany, to take in more Syrian asylum seekers from Turkey.

At home, Merkel has already vowed to speed up deportations of migrants who are not fleeing war. In the past 12 months, more than a million migrants from the Middle East and beyond have sought sanctuary and jobs in Europe’s economic powerhouse. Yet in a sign that public tolerance may be growing thin, voter turnout was up Sunday, and above 70 percent in two of the states voting.

“The results will probably further fuel the existing unease with Merkel within her own CDU,” said Carsten Nickel, senior vice president of Teneo Intelligence.