Germany's far-right AfD has won its first regional election, taking between 30.5 and 33.5 percent of the vote in the former East German state of Thuringia, exit polls showed on Sunday.

The party is also neck-and-neck with the conservative CDU for first place in the state of Saxony, which also held a regional election on Sunday, the polls showed.

Chancellor Olaf Scholz's Social Democrats (SPD) meanwhile looked to have scored a disappointing result in both states of between 6.5 and 8.5 percent.

Voters in Thuringia and Saxony, two former East German states, cast ballots in elections that could significantly impact Chancellor Olaf Scholz's government, with the far-right Alternative for Germany (AfD) expected to make substantial gains amid growing debate over immigration following a recent suspected Islamist attack.

An election victory for the AfD would be a landmark in Germany's post-war history and represent a rebuke for Scholz ahead of national elections in 2025.

In both states, Scholz's Social Democrats are polling at around six percent, while their coalition partners, the Greens and the liberal FDP, lag even further behind.

But even if the AfD does come out on top in the elections, it is unlikely to come to power because other parties have ruled out working with the far right to form a government.

This is a developing story, more to follow.