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.

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