The leaders of eight German states have backed the nation’s chancellor amid growing speculation about his political future.

The premiers – all of whom are part of Friedrich Merz’s Christian Democratic Union (CDU) – wrote that restoring trust in their party lay in “listening ​and taking political action, not in debates ​over personnel”.

Merz, who has only held the post for 16 months, is facing poor approval ratings while the anti-immigration, far-right Alternative for Germany (AfD) party is surging, prompting questions about whether he is an electoral liability.

He has vowed to carry on but two more state elections on Sunday have been seen as a key test of his leadership.

Rumours of a “Kanzlertausch” – or “Chancellor swap” – have been around for months, but they have increased since the conservative CDU tumbled to a distant second behind the AfD in the eastern state of Saxony-Anhalt at the start of September.

The AfD shot up to 43.8% of the vote while the CDU plummeted to 17.2%, marking the first time since World War Two that a far-right party has come close to controlling a German state.

It is still three seats short of an outright majority and the major parties would not enter into a coalition with the AfD, though it could seek to form a minority government.

Merz came out fighting after the loss, describing the AfD – which wants to rebuild ties with Russia – as a “destructive force” whose migration policy amounted to an “ethnic cleansing” of skilled workers.

The AfD responded to his remarks by saying it was filing a defamation complaint against the chancellor over what it described as “baseless” and “disgusting” claims.

The chancellor’s abrasive communication style and personal unpopularity – with just 14% thinking he is right for the job, according to a recent Bild poll – have raised questions about his viability as leader of both Germany and the CDU.

The CDU’s eight state premiers wrote, however, that “now more than ever, ⁠Germany’s political landscape needs stability”.

“Our country will continue to need a stable and effective federal government with its own majority in the Bundestag [German parliament],” said the leaders of Schleswig-Holstein, Saxony, Hesse, Rhineland-Palatinate, Saxony-Anhalt, Thuringia, Berlin and North Rhine-Westphalia.