The German chancellor, Olaf Scholz, has urged mainstream parties not to lend support to the far-right Alternative for Germany (AfD) party, which won a big victory in the eastern state of Thuringia in Sunday’s regional election.

The result gives the far right its first win in a state parliament election since World War Two.

The AfD also came a close second in Sunday’s other big state election, in the more populous neighbouring state of Saxony.

On Monday, Mr Scholz urged other parties to block the AfD from governing by maintaining a so-called firewall against it.

“All democratic parties are now called upon to form stable governments without right-wing extremists,” he said, calling the results “bitter” and “worrying”.

The AfD has been classified as right-wing extremist by domestic intelligence in Thuringia and in Saxony. In May, a German court ruled that intelligence officials were justified in placing the AfD under observation for suspected extremism.

AfD co-leader Alice Weidel said that voters in Thuringia and Saxony had given her party a “very clear mandate to govern”.

She urged parties to ignore Mr Scholz’s call to build government coalitions without the AfD, and said that doing so would “undermine the democratic participation of large sections of the population”.

“Firewalls are undemocratic,” Ms Weidel added.

Without the support of other parties, the AfD cannot govern in Thuringia.

The second-largest party, the conservative CDU, has made clear it will not consider ruling with the far right.

Mathematically, then, the conservatives will need support from parties on the left to form a majority.

They have previously refused to work with the left-wing Die Linke, meaning they could have to look at the more radical left populist Sahra Wagenknecht’s BSW to form a ruling coalition – an unpalatable option for many within the CDU.

Björn Höcke, the AfD’s top candidate in Thuringia and a highly controversial figure in Germany, has suggested there were plenty of CDU voters who would be happy if they worked together instead.

In any case, with over 30% of the vote the AfD has a so-called “blocking minority” – meaning it will be able to stop the appointment of new judges or any constitutional change.