Washington DC - President Donald Trump on Tuesday hailed what he called a "really big" victory by Germany's far-right movement after the Alternative for Germany (AfD) party scored an upset in state elections.

"Wow! The Populist Party in Germany just had a really big night," Trump posted on his Truth Social platform, before going on to bash the country's immigration regulations.

"They finally got tired of the absolutely horrible Immigration rules and regulations which have hurt Germany so badly."

Trump's celebratory post – which did not name the party specifically – came two days after the AfD emerged as the largest party in elections in the eastern state of Saxony-Anhalt.

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The anti-immigration and pro-Trump AfD party took almost 44% of the vote, and has vowed a "remigration and deportation offensive" targeting migrants.

The prospect of the first far-right government taking charge of a German state since World War II has deeply unsettled many migrants and minority groups.

The AfD in Saxony-Anhalt is labeled a "right-wing extremist" group by Germany's domestic intelligence agency, and its triumphant lead candidate Ulrich Siegmund's staff are known former members of a since-banned neo-Nazi organization.

Trump supporters have cheered on the AfD, with former US ambassador to Germany Richard Grenell celebrating the results as "a new day in Germany" and tech billionaire Elon Musk rushing to be among the first to celebrate AfD's victory with a resounding "Well done!"

"THEY ARE ON THE RISE, and not going to take it anymore! MGGA!!!" Trump posted on social media, a German variation on his "Make America Great Again" slogan.