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.

It comes after Markus Söder, the premier of Bavaria and leader of the CDU’s sister party the CSU, stood by Merz.

An unnamed party source told news agency Reuters that CDU officials will meet on Sunday to co-ordinate the party’s response to the results of that day’s state elections in Berlin and Mecklenburg-West Pomerania – where the AfD is poised for further gains and the CDU for further losses.

However, the race is far more evenly split in the German capital than it was in Saxony-Anhalt, with the CDU and Die Linke (The Left) vying for first place, and the AfD and Greens not far behind, according to polls.

In Mecklenburg-West Pomerania, polls put the AfD ahead of the centre-left SPD but likely well short of an outright majority.

The worst-case scenario for Merz would be for the CDU to lose power in Berlin and not get enough votes to even have a presence in Mecklenburg-West Pomerania’s parliament.

Unlike in the UK, Germany is not well-versed in replacing its leader mid-term, though Merz could, in theory, be pressured to resign or face a vote of no confidence, though many regard that outcome as unlikely.

No one within the CDU has yet said they were willing to challenge Merz, but the speculation about his future has led to several names – including Söder, North Rhine-Westphalia premier Hendrik Wüst and German Interior Minister Alexander Dobrindt – being touted as potential successors.

Even before Merz had officially been made chancellor, he managed to rally support for a massive €500bn ($547bn; £420bn) defence infrastructure fund, with his straight-talking style and focus on European security earning him plaudits on the world stage.

But it took him three attempts to become CDU leader and he then lost an initial vote to become chancellor despite technically having sufficient votes through a coalition deal with the SPD. It was a first in post-war Germany.

This suggests that he has a history of struggling to appeal to even those within his own ranks – and that he may be unlikely to let go of a job he has long coveted.