The far-right Alternative for Germany party, or AfD, has won its biggest success yet after claiming victory in the election for the Saxony-Anhalt regional assembly, but now faces the challenge of how to form a local government after failing to secure an outright majority.

Germany is a federation of 16 states, which have a degree of autonomy over issues such as culture, local education and policing. In Saxony-Anhalt, a state to the west of the capital Berlin, the AfD won 43.8 percent of the vote, taking 39 out of the 82 seats available, with voter turnout notably high, at 77.8 percent.

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The mainstream conservative Christian Democratic Union-Christian Social Union, Chancellor Friedrich Merz's coalition, was the only other party to win seats in double figures in that state, with 15, putting it in a difficult position of forming the next local government, as mainstream parties have traditionally refused to work with the far right.

AfD local leader Ulrich Siegmund called the result "sensational" and said the party had won a mandate to govern, adding "this isn't just about Saxony-Anhalt …It's a signal for the whole of Germany — a self-confident signal".

The party's national coleader Tino Chrupalla said Siegmund "will definitely run as a candidate for state premier in the state parliament. That much is certain", and if the AfD failed to form a government, he said there could be another vote, which he predicted would be even more in the AfD's favor.

German Chancellor Friedrich Merz said the election victory had shaken his party to its core and signaled that a major reckoning was needed, the Bild newspaper reported on Monday.

"This shakes our party to its very foundations," Merz said, according to the newspaper.

The result was shared on social media by United States President Donald Trump, and the US business tycoon Elon Musk also congratulated the party on its win, with Siegmund replying and thanking Musk "for your support and for your clear and highly important perspective on the political developments of our time".

Although voters in Saxony-Anhalt only make up 3 percent of the German population, the result will send shock waves across Europe, as it is the biggest electoral success for the far right in Germany since World War II. While AfD supporters and other European populist right parties celebrated, others were vocal in their dismay.

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Eva Umlauf, president of the Berlin-based International Auschwitz Committee and a survivor of the Holocaust, was quoted as saying, "This election result scares me… What path is Germany on? The one that it traveled before?"

In France, government ministers expressed their worries on Monday over the impact of the victory of AfD. "It clearly sends out a very, very worrying signal," French Finance Minister Roland Lescure told RTL radio.

Agencies contributed to this story.

Contact the writers at julian@mail.chinadailyuk.com