The 11-year-old AfD, which has greater support in the formerly communist-run east, will be unlikely to be able to form a state government even if it does win, as it is polling short of a majority and other parties refuse to collaborate with it.
But it will be the first time a far-right party has the most seats in a German state parliament since World War II and its strength will complicate coalition building and could allow it to block constitutional changes and appointments of some judges.
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The AfD is polling 30 percent in Thuringia, nearly 10 points ahead of the conservatives in second place, while tying with them in Saxony on around 30-32 percent. The newly-created far-left Sahra Wagenknecht Alliance (BSW) is set to come third in both states.
Strong gains for the two anti-establishment parties herald growing instability in Europe's biggest economy, reflecting a fragmentation of the political landscape that could also complicate efforts to form coherent national governments.
The AfD's signature topic of migration shot up the agenda after a knife attack a week ago in the western city of Solingen in which a 26-year-old suspected Islamic State member from Syria is accused of killing three people.
"We want to end the failure of the state, the loss of control," AfD co-leader Alice Weidel told a campaign event on Wednesday in Dresden. "That can only be done through a sustainable change in migration and asylum policy."
All three parties in Scholz's federal coalition are expected to lose votes and two may even struggle to make the 5 percent threshold to enter parliament. Their sagging popularity could mean a return to a conservative-led alliance in next year's national polls.
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Business leaders have warned of the threat of far-right extremism to Europe's largest economy, saying it could make it harder to attract skilled labor and investment. German politicians say populist rhetoric has fueled physical attacks.
The AfD is led in Thuringia by Bjoern Hoecke, a man that some in the party considered so extremist they tried to expel him.
The former history teacher has called Berlin's memorial to Nazi Germany's Holocaust of Europe's Jews a "monument of shame" and was convicted earlier this year for using a Nazi slogan at a party rally.
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While voting patterns in the formerly communist-run east are still distinct 30 years after reunification due to weaker party allegiances and greater economic pessimism, Sunday's elections give a flavor of nationwide and even European-wide trends.
