German Chancellor Angela Merkel | Axel Schmidt/Getty Images Angela Merkel says AfD ‘a problem, not a threat’ Chancellor says far-right party benefited from protest votes.

German Chancellor Angela Merkel on Monday dismissed the rise of Alternative for Germany, describing the far-right party as a "problem" not a "threat" to the Christian Democrats.

Alternative for Germany (AfD) was the big winner in elections in three federal states on Sunday, extending its representation to eight or half of the state parliaments in Germany. The big loser of the night was Merkel and her Christian Democrats (CDU).

"Yesterday was a terrible day for the CDU," the chancellor acknowledged in a speech in Berlin on Monday.

She said the success of the AfD was in part down to protest votes against her migration policy and discontent toward traditional parties. However, she said the AfD was a "problem" not an "existential threat."

The result sparked debate within the center-right, with Horst Seehofer, who heads the Christian Social Union, the Bavarian sister party of the CDU, attributing the election setback to the chancellor's refugee policy.

“The main reason is the refugee policy. It makes no sense to avoid talking about it,” Seehofer said Monday. The center-right has to strengthen its conservative values so voters "will not remain homeless," he added.

Seehofer, the Bavarian premier, urged a change of course by Merkel. "We need a different policy," he said.

Merkel disagreed, saying the elections highlighted the worrying split between CDU and CSU. "These differences are hard to bear for the voters of the union,” she said.

She also defended her controversial migration policy, saying although there was "fear of another religions, fear of Islam" and uncertainty in Germany because of "changes in many established structures," she "remains convinced that a European solution [to the problem] is needed."

Her spokesman, Steffen Seibert, said the refugee policy is to be continued both at home and abroad.

The CDU suffered crushing defeats in Baden-Württemberg and Rhineland-Palatinate. It managed to hold onto Saxony-Anhalt, but suffered losses there compared to the last election five years ago.

The AfD won 24.2 percent of the vote in Saxony-Anhalt, 15.1 percent in Baden-Württemberg and 12.6 percent in Rhineland-Palatinate.