BERLIN (Reuters) - Support for one of Germany’s ruling parties has sunk to a near 20-year low and Chancellor Angela Merkel’s conservatives have lost ground too, a poll showed on Thursday, suggesting a deal to limit migrant numbers has yet to reassure voters.

Slideshow ( 2 images )

Merkel is banking on the success of the deal between the European Union and Turkey which gives Ankara political and financial benefits in return for taking back refugees and migrants who had crossed to Greece.

Both Chancellor Merkel’s conservative bloc (CDU/CSU) and her Social Democrat (SPD) junior coalition partners suffered heavy losses in three state elections last month while voters flocked to the anti-immigrant Alternative for Germany (AfD) party.

The Deutschlandtrend poll for public broadcaster ARD/WDR showed voters remained fed-up with infighting within the ruling coalition about how to handle the crisis and integrate the new arrivals.

Support for the CDU/CSU fell 2 percentage points to 34 percent, the lowest level in nearly four years, while the SPD sank 2 percentage points to 21 percent, its lowest ever level in the ARD poll, which has been carried out since 1997.

Meanwhile, support for the AfD rose 3 percentage points to 14 percent, its highest ever level in the poll.

Gero Neugebauer, a political scientist at Berlin’s Free University, linked the waning support for Merkel’s conservatives and the co-governing SPD to the quarrels within the coalition on migration policy.

“The voters are punishing the ruling parties because the coalition is a constant dispute,” Neugebauer said. “The public perception of the coalition is really bad.

“Many have doubts that the EU/Turkey agreement has the potential to solve the refugee crisis. The majority of Germans is skeptical on this.”

The poll of 1,505 people was conducted by Infratest-dimap between Monday and Wednesday.