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 rule 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, but it will depend on which of the smaller parties get into the state parliament before the party’s leaders know if they have enough seats to govern.

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.