MAGDEBURG, Germany — An eastern German region voted Sunday in an election that could bring to power the first far-right state government in the nation’s post-World War II history.

The vote for the state legislature in Saxony-Anhalt, a region of 2.1 million people west of Berlin, has gained outsized prominence because it represents the best chance yet of a governor’s post for the far-right, anti-migration Alternative for Germany, or AfD.

That would be the biggest prize in the party’s 13-year history, at a time when there’s widespread discontent with an unpopular national government that has yet to persuade voters it can get the country’s sluggish economy moving. It would be at least a symbolic blow to Chancellor Friedrich Merz, whose center-right party has led Saxony-Anhalt for 24 years.

AfD is the biggest opposition party in Germany’s national parliament and is strongest in the formerly communist and less prosperous east, where Saxony-Anhalt is located. Its candidate for governor, Ulrich Siegmund, declares that “we will write history here.”

Despite consistently strong support, though, its chances of taking power are uncertain even if it finishes well ahead of its opponents.

On Sunday, AfD hopes to win an absolute majority in the state legislature. That would overcome the so-called “firewall” of mainstream parties’ refusal to work with AfD, whose regional branch is one of several classified by the domestic intelligence agency as a proven right-wing extremist group. AfD vehemently rejects accusations of extremism.

The party’s national co-leaders, Alice Weidel and Tino Chrupalla, said this week that AfD “wants to implement the law of the land — for example with a view to illegal migration — and ensure that Germany remains worth living in.” They decried other parties’ records and argued in a statement that an absolute majority for AfD is “almost the only chance to change course.”

Merz said an AfD government would be an economic own-goal. “If there were to be an absolute majority for a right-wing populist party next Monday, then international investors will think three times about whether they still invest in Saxony-Anhalt,” he said.

Siegmund says he will only seek election as governor by state lawmakers if AfD wins an absolute majority, arguing that it needs to break a pattern of parties breaking their preelection promises.

Whether it can win that majority is expected to depend in part on whether parties such as the center-left Social Democrats and Greens top the 5% support needed to keep parliamentary seats. If there is no absolute majority for AfD, the party is unlikely to find a coalition partner.

Incumbent governor Sven Schulze, from Merz’s Christian Democratic Union, says he won’t work with the far-right party and his own CDU is “100%” behind him. But, if AfD finishes first yet short of a majority, he’s likely to face a difficult task to put together a stable government.

There has already been one case in which AfD finished first in a state election but didn’t end up governing. That was two years ago in neighboring Thuringia, where a CDU governor took power with a minority government.

Schulze could, in similar circumstances, try to put together some kind of alliance with smaller parties. It’s likely to be a delicate exercise, because it would probably require at least some tacit support from the Left Party, a hard-left party with which the CDU refuses to form coalitions.

Sunday’s vote will be followed on Sept. 20 by two more tricky tests for Merz’s CDU and its main partners in the national government, the Social Democrats.

There are state elections that day in Mecklenburg-Western Pomerania, an eastern region where a center-left government faces a strong challenge from AfD, and in Berlin, currently led by Merz’s party.

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Moulson reported from Berlin.