While the anti-immigration AfD eased into state parliaments in Baden-Württemberg, Rhineland-Palatinate and Saxony-Anhalt, Germany's other parties saw substantial losses on Sunday.

The results mean that the mainstream parties - especially Angela Merkel's Christian Democratic Union (CDU), the center-left Social Democrats (SPD), and the Greens - will need to seek new and possibly uncomfortable alliances to establish coalition governments in the three states.

None of these, however, will include the AfD, as all the mainstream parties made clear ahead that they would not join a coalition with the party.

Not all bad for Merkel

Despite the triumph for the AfD, a majority of the electorate backed parties taking a pro-asylum stance. Not only that, the CDU candidates who distanced themselves from Merkel the most, Julia Klöckner in Rhineland-Palatinate and Guido Wolf in Baden-Württemberg, took the biggest losses.

Klöckner had made headlines during the campaign for her so-called "Plan A2" for dealing with refugees - a day-quota system that watered down Merkel's refusal to cap refugee numbers.

As a result, critics accused her of wavering between support and opposition to Merkel. But on Monday, Klöckner defended her plan. "We would have lost even more to the AfD if we hadn't taken a clear position on the question," she said.

Chancellor Merkel herself refused to make changes to her refugee policies as a result of the election. "The federal government will stay its refugee policy course ... at home and abroad," her spokesman Steffen Seibert told a news briefing on Monday.

Merkel allies demand change

Nevertheless, Merkel admitted that fears associated with the refugee crisis had damaged her party in the elections. At her own briefing on Monday after consulting with her party committees, she conceded the votes for the AfD had been a protest against the "unresolved questions over the many refugees, and fears with regard to integration."

She also admitted that for many people, the government had not found a "conclusive and satisfying solution" to the issue.

But her Bavarian ally Horst Seehofer, head of the Christian Social Union, struck a more panic-stricken note, demanding a change of course from the chancellor and even questioning the future of the conservative alliance between his party and the CDU. "We need a different policy," Seehofer said at a press conference in Munich. "This is about our existence. The descent could become a nosedive, it could become a crash."

Merkel rejected the warning. "I don't see it as an existential problem for the CDU, but I see it as a problem," she said. What her party needed was an "argumentative debate, but a clear demarcation."

SPD bullish, CDU wary, Jewish council alarmed

SPD chief and Vice Chancellor Sigmar Gabriel, whose party won in Rhineland-Palatinate but was beaten into fourth place elsewhere, took a combative tone, and vowed not to chase new AfD voters. "We won't run after the populists," Gabriel said in Berlin on Monday. "We will do everything to keep the democratic center in Germany stable."

He added that the AfD belonged in a gray zone between "German nationalists, right-wing populists and far-right radicals."

But other CDU chiefs were taking the results as a warning, even in victory. "There should be no democratic alternative to the right of the CDU," said Saxony-Anhalt's incumbent state premier Reiner Haseloff, who held onto his post on Sunday. "We cannot keep going as we are," he added.

CDU deputy leader Armin Laschet said the results showed that politicians needed to work harder "to explain their policies, and maybe they need to find a new style in the way they treat each other."

At the same time, Laschet maintained that mainstream politicians must not ape the AfD's rhetoric.

Kretschmann took a similar line. "We have to do everything to stop the right-wing populists creeping into the middle of society," he said in Stuttgart.

Germany's Central Council of Jews was also alarmed at the results. "The fact that an out and out right-wing populist party, which occasionally tolerates far-right positions, gets so many votes shows a frightening rightward shift in society," its president Josef Schuster told the DPA news agency. "The widespread sentiments against refugees and the fears of something foreign have helped the AfD to undeservedly high election results."

AfD rejects parallels with Front National

For its part, the AfD declined to draw parallels with right-wing parties in the rest of Europe, and distanced itself from the Front National in France.

During a testy exchange with reporters at a press conference in Berlin on Monday, leader Frauke Petry said that the "endless label debate" was less productive than talking about policies, while spokesman Jörg Meuthen said that the French party had shown nationalist and socialist tendencies which the AfD did not share.

In addition, addressing the allegations of the "lying press" that her supporters have leveled against the media, Petry called for journalists to take a "less ideological approach" to its reporting on the AfD.