Germany’s AfD is heading for a big victory in the eastern state of Saxony-Anhalt, far ahead of its mainstream rivals, exit polls say. It is not yet clear if that would be enough to take power in the state but the AfD says it has won a mandate to govern.

The far-right party is projected to win 44-44.5% of the vote, far ahead of the conservative CDU on 18.5%.

The AfD has hailed the result as a “historic outcome” and the charismatic leader in the state, Ulrich Siegmund, has refused to govern with any other party.

No far-right party has won control of a state in Germany since World War Two, and governing at state level would mean powers over policing, local education and culture.

Saxony-Anhalt has a small population of 2.1 million and the AfD in the state is assessed by domestic intelligence as “far-right extremist”, a classification rejected by Siegmund.

The AfD’s projected result is higher than earlier opinion polls suggested, and Siegmund along with joint national leaders Alice Weidel and Tino Chrupalla were overjoyed as the news emerged.

However, party leaders will not know if they have enough seats to govern until they see which of the smaller parties get into the state parliament.

That may hinge on whether one of the smaller parties gets over the required threshold of 5%. If it fails, then the AfD’s chances of a majority increase.

A crowd of supporters at the AfD election night party HQ erupted in cheers as the projections came up on the screen.

A short while later, people burst into singing Germany’s national anthem.

“We have made history in this state,” Siegmund said. His opposite number in the CDU, Sven Schulze, conceded victory and said his party would have to deal with the result: “This was an extremely tough and intensive election campaign.”

The AfD has not only dominated the election campaign, it is emerging as the dominant force in the result as well. Although the outcome was initially unclear, the party’s supporters believe they are on the march.