Tens of thousands demonstrated across Germany against far-right extremism on Saturday, with major rallies held in Dusseldorf, Hamburg, Berlin and Munich, almost a week after the Alternative for Germany (AfD) party's historic election win.

Sunday's election win for the AfD in the Saxony-Anhalt election, where they earned 44% of the vote, brought Germany's far right closest yet to gaining power since World War II.

In Dusseldorf, around 20,000 people took part in a protest march "against the AfD and right-wing hatred," according to police and organizers, while organizers said a further 25,000 marched in Hamburg.

In Berlin, several marches against the normalization of right-wing politics converged on the city's town hall. Police put the number of participants at 18,000, while organizers said 32,000 took part.

In several cities, rallies were also held as part of the nationwide initiative demanding that Germany's Constitutional Court review parties suspected of being or confirmed to be far-right extremist by Germany's domestic intelligence agency. These demonstrations, organized by the group PRÜF, which translates as proof or check, take place on the second Saturday of each month in German state capitals.

The largest of these rallies on Saturday was in Munich, where police said around 12,000 people gathered. Around 2,000 came together in Mainz, around 1,500 in Saarbrücken and around 1,100 in Magdeburg. Protests were also held in Leipzig and Saarbrücken.

The AfD is monitored nationwide by the domestic intelligence agency as a suspected extremist organization. Several of its state branches, including those in Thuringia and Saxony-Anhalt, are classified as far-right extremist.

Following the AfD's election success in Saxony-Anhalt, North Rhine-Westphalia state premier Hendrik Wüst proposed setting up a joint federal-state working group to examine whether a ban on the party could be pursued. The proposal has won support from some politicians but has also met with scepticism.

Only the Bundestag, the lower house of parliament, the Bundesrat, the upper house, or the federal government can apply to the Federal Constitutional Court for a party to be banned. Any ban would be decided by this court.