A far-right party won a state election for the first time in post-World War II Germany on Sunday and looked set to finish a very close second to mainstream conservatives in a second vote.

A new party founded by a prominent leftist also made a strong impact, while the parties in Chancellor Olaf Scholz’s unpopular national government obtained extremely weak results.

The far-right Alternative for Germany, or AfD, won 32.8 percent of the vote in Thuringia in the country's east — well ahead of the centre-right Christian Democratic Union (CDU), the main national opposition party, with 23.6 percent.

In neighbouring Saxony, projections put support for the CDU, which has led the state since German reunification in 1990, at 31.9 percent and AfD on 30.6-30.7 percent.

AfD made substantial gains in Thuringia and smaller ones in Saxony compared with the last state elections in 2019.

“An openly right-wing extremist party has become the strongest force in a state parliament for the first time since 1949, and that causes many people very deep concern and fear,” said Omid Nouripour, a leader of the Greens, one of the national governing parties.

Other parties say they won't put AfD in power by joining it in a coalition.

Even so, its strength is likely to make it extremely difficult to form new state governments, forcing other parties into exotic new coalitions.

“This is a historic success for us,” Alice Weidel, a national co-leader of AfD, told Germany media. She described the result as a “requiem” for Scholz's coalition.

The CDU's national general secretary, Carsten Linnemann, said that “voters in both states knew that we wouldn't form a coalition with AfD, and it will stay that way — we are very, very clear on this."

Weidel denounced that as “pure ignorance” and said that “voters want AfD to participate in a government.”

Deep discontent with a national government notorious for infighting, anti-immigration sentiment and scepticism toward German military aid for Ukraine were among the factors that have contributed to support for populist parties in the region, which is less prosperous than western Germany. (AP)