The far-right Alternative for Germany (AfD) is "very, very close" to taking power, its deputy parliamentary leader has told the BBC, after a historic victory in elections for the eastern state of Saxony-Anhalt.

Sunday's preliminary results show it fell three seats short of an outright majority, with 43.8% of the vote. It is now seeking support from other parties or individuals in order to govern.

While most German political parties refuse to work with the AfD, Beatrix von Storch called for its opponents to enter talks and said: "You cannot say I do not accept the vote of the people".

No far-right party has controlled a German state since World War Two, and governing at state level would mean powers over policing and local education.

Von Storch said if parties refused to work with the AfD, "then we might end up in severe chaos and maybe we have a new election".

Her comments were echoed by AfD's leader in Saxony-Anhalt, Ulrich Siegmund, who told a news conference on Monday that the party had won a "clear mandate to govern".

Saxony-Anhalt has a small population of 2.1 million and the AfD in the state is assessed by domestic intelligence as "right-wing extremist", a classification rejected by Siegmund, 35.

Siegmund said discussions with other parties were initiated on Sunday night and could potentially take days or weeks to conclude.

"We reach out to everybody first, we will have consultations and then we'll see whether [there are] individual parliamentary groups or MPs who would be willing to help us," he added.

The AfD is currently heading for 39 seats in the 83-seat state parliament instead of the 42 needed for an outright majority, although the result has not yet been finalised.

Von Storch told the BBC the AfD was talking to individuals within the conservative CDU group – the largest party in both the state's outgoing coalition and Germany's government – because they were "very, very unhappy with their own party".

In Saxony-Anhalt, the CDU won 17.2% of the vote, according to preliminary results.

One idea being floated is whether there could be informal deal whereby a small party – the BSW – could give their tacit support to allow the AfD to form a minority government.

The left-wing populist BSW, which is set to win five seats, is also tough on migration and backs importing Russian gas.

The AfD has signalled an openness to talk with other parties but all – apart from the BSW – refuse to co-operate with the far-right.

The AfD leads the opinion polls nationally, ahead of the ruling conservatives of Chancellor Friedrich Merz and the Social Democrats, but their heartland lies in the eastern states.

They also won the 2024 state election in neighbouring Thuringia, but failed to secure enough seats to win power.

Among the AfD's policies is a highly controversial plan for "remigration", which is widely understood to mean mass deportations of migrants, although the party says it refers to deporting criminals and those in the country illegally.