BERLIN - Voters punished Chancellor Angela Merkel's conservatives in three German regional elections on Sunday, giving a thumbs-down to her open-door refugee policy and turning in droves to the anti-immigrant Alternative for Germany (AfD).

A carnival float with papier-mache caricatures mocking Bavarian Governor Horst Seehofer and German Chancellor Angela Merkel is displayed at a postponed "Rosenmontag" (Rose Monday) parade, at one location in Duesseldorf, Germany, March 13, 2016, after the original parade in February was cancelled due to severe weather. Words read 'crucify her' 'human politics for migrants'.  [Photo/Agencies]

The result is a big setback for Merkel, who has led Europe's biggest economy for a decade, and could narrow her room for manoeuvre as she tries to convince her European Union partners to seal a deal with Turkey to stem the tide of migrants.

Merkel's Christian Democrats (CDU) lost ground in all three states - Baden-Wuerttemberg and Rhineland-Palatinate in the west and Saxony-Anhalt in the east - which were together widely seen as offering a verdict on Merkel's liberal migrant policy.

"These results are a serious rebuke for Merkel and the most pronounced protest vote we've seen so far," said Holger Schmieding, an analyst at Berenberg Bank.

The result in the two western states was the worst-case scenario for Merkel, who has staked her legacy on her decision to open Germany's doors to over 1 million migrants last year. But she still looks set to run for a fourth successive term as chancellor, with no real challenger for the right to lead her party into next year's federal election.

"The result will increase the noise within the CDU and constrain the government's options on migrants and Greece, but Merkel's chancellorship is not at risk," said Carsten Nickel at Teneo Intelligence.

Responding to voters' fears, she has promised to stem the flow of migrants to Germany, and is trying to convince Turkey to help - and other EU partners to share the burden. In the last few weeks, the numbers of migrants entering Germany have fallen.