Chancellor Angela Merkel's conservatives won a resounding victory in a state election in eastern Germany on Sunday, boosting conservative leader Armen Laschet, who hopes to succeed her in September's national election.

An exit poll for public broadcaster MDR had the Christian Democrats (CDU) on 36%, up more than 6 points on five years ago, and far ahead of the far-right Alternative for Germany (AfD), who was on 22.5%, slightly down on the previous election.

The CDU under new party chief Armin Laschet won between 35 and 36% of the vote, exit polls showed, with the anti-immigration party on between 22.5 and 23.5%.

Meanwhile, support for the far-right Alternative for Germany (AfD) slipped in a key state election but remains the second-biggest bloc in the regional parliament.

Support for the AfD in the small eastern German state of Saxony-Anhalt edged down to 23.5% from the 24.3% it secured in the last election five years ago.

Underscoring the strong backing for the AfD in the country's formerly communist east, the Saxony-Anhalt result is about double the party's current standing as measured by a slew of national opinion polls.