Worries about the economy and migration pushed up share for far-right AfD in Hesse and Bavaria, while coalition parties did worse

German chancellor Olaf Scholz’s fractious centre-left coalition has received a sharp rebuke from voters in the key states of Bavaria and Hesse, with economic woes and immigration fears boosting the opposition conservatives and the far right.

At the elections on Sunday the far-right Alternative for Germany (AfD) party burst out of its post-industrial eastern strongholds to score its best ever result in a western state. Polls showed it on course to be the second largest party in Hesse, home to the financial capital Frankfurt.

All three parties in Scholz’s federal coalition – his Social Democrats, the Greens and the pro-business Free Democrats (FDP) – did worse than five years ago in the states, which together account for about a quarter of the German population.