DAVOS, Switzerland (Reuters) - German Chancellor Olaf Scholz said on Tuesday he does not support freedom of speech when it is used for extreme-right views, a day after a hand gesture by U.S. billionaire Elon Musk caused uproar during Donald Trump's inauguration festivities.

"We have the freedom of speech in Europe and in Germany. Everyone can say what he wants, even if he is a billionaire. And what we do not accept is if this is supporting extreme-right positions," Scholz said in Davos when asked about the incident.

Musk's hand gesture during a celebration of President Trump's inauguration drew online comparisons to a Nazi salute.

Musk dismissed the criticism as a "tired" attack.

"Shame on Oaf Schitz," Musk posted on X, the platform he owns, on Tuesday with a video clip shared by another user that showed Scholz speaking at the annual meeting of the World Economic Forum in the Swiss resort.

"Schitz" has no meaning in German.

Musk has previously attacked Scholz on X, calling him an "incompetent fool" who should resign after a deadly attack at a German Christmas market.

He has also used the platform formerly known as Twitter to signal his support for the far-right Alternative for Germany (AfD) party ahead of elections scheduled for next month.

Musk's repeated endorsement of the AfD, the party that has embraced the Trump administration most among German parties, has drawn ire in Berlin, but the German government has stopped short of unanimously leaving his platform.

The European Commission said this month that it was stepping up its investigation into whether X breached European Union rules on content moderation.

Musk's hosting of AfD leader Alice Weidel for a discussion on X this month was watched by the European Commission to check for any spreading of misinformation.

(Reporting by Miranda Murray; Writing by Rachel More; Editing by Alexander Smith)