Musk, speaking by video link, told thousands of AfD supporters gathered in the eastern city of Halle that their party was “the best hope for the future of Germany”.

AfD supporters at the rally shouted their approval as party co-leader Alice Weidel looked on smiling.

Meanwhile, protesters against the AfD turned out in cities across Germany.

The largest gatherings took place in Berlin and Cologne, police revising their turnout figures upwards to 35,000 and 40,000 respectively. Organisers in Berlin claimed that 100,000 people attended the protests in the capital.

The protesters there used their mobile phones to form “a sea of light for democracy” in front of the Brandenburg Gate, brandishing letters forming the word “Resistance”.

AfD is polling at around 20 percent ahead of Germany’s February 23 elections, a record for a party that has already shattered a decades-old taboo in post-war Germany against supporting the far right.

The mainstream conservative CDU/CSU alliance leads on about 30 percent, with CDU leader Friedrich Merz the favourite to become chancellor after the elections.

– Protests across Germany –

Musk, a close associate of US President Donald Trump, told the AfD rally: “I think this election coming up in Germany is incredibly important.

“I think it could decide the entire fate of Europe, maybe the fate of the world.”

Musk has rattled European politicians in recent weeks with comments on his social platform X supporting AfD and far-right politicians in other countries, including Britain.

He also drew attention this week for making a public gesture some observers interpreted as a straight-armed Nazi salute, a claim he himself dismissed as a smear.

Like Trump, the AfD opposes immigration, denies climate change, rails against gender politics and has declared war on a political establishment and mainstream media it claims limit free speech.

The anti-AfD rallies took place in some 60 towns following calls from a variety of organisations, attracting more people than the police had initially expected.

The protests passed off peacefully, with banners saying “Nazis out” or “AfD is not an alternative”, a reference to the far-right party’s full name “Alternative for Germany”.

The CDU’s Merz also came in for criticism. Many protestors fear he is tempted to break his party’s policy of refusing to enter into coalition talks with the AfD.

There was also a protest in the southern city of Aschaffenbourg, where a deadly knife attack this week by an Afghan migrant further inflamed the debate over immigration.

Several thousand also turned out in the eastern city of Halle, where the AfD rally was addressed by Musk, leading to a few incidents.

Halle police said they had opened criminal investigations for offences including assault, insults and disrupting traffic. They said they would also be taking action against 21 people who tried to force a barrier.

Musk told the AfD rally that “the German people are really an ancient nation which goes back thousands of years”.

“I even read Julius Caesar was very impressed by the German tribes,” he said, urging the supporters to “fight, fight, fight” for their country’s future.

He said the AfD wanted “more self-determination for Germany and for the countries in Europe and less from Brussels”, a reference to what he sees as heavy handedness from European Union regulators.

Weidel told her rally that migrants in Germany had to be sent home.

“We need re-migration to live safely in Germany,” she said.