Beatrix von Storch, deputy leader of AfD party, could be charged with incitement to hatred, and was temporarily banned from Twitter and Facebook.
A far-right German MP is under police investigation over inflammatory anti-Muslim comments she made on social media on New Year’s Eve.
The Twitter account of Beatrix von Storch, deputy leader of Germany’s AfD party, was temporarily suspended on Monday, but she was later posting again on the site.
Von Storch accused Cologne police of appeasing “barbaric, gang-raping Muslim hordes of men” after they tweeted a new year message in Arabic. The police also tweeted the message in other languages, including English, French and German.
The authorities are considering whether Von Storch should be charged with incitement to hatred, a criminal offence.
Her Twitter account was suspended for 12 hours for her post, as it breached the site’s rules. On her return to the social media site, Von Storch posted in German: “Facebook has now also censored me. This is the end of the constitutional state.”
Germany has enacted stringent hate speech laws, with social media firms facing fines of up to €50m (£44m) if they do not remove “obviously illegal” hate speech and other postings within 24 hours of receiving a notification.
In June, von Storch answered “yes” to a question on Facebook asking whether firearms should be used against women and children trying to cross the German border.
Von Storch, whose grandfather served as finance minister under Hitler, later suggested her computer mouse had slipped.
She posed with former Ukip leader Nigel Farage when he launched AfD’s German election campaign in September. Farage described chancellor Angela Merkel’s decision to keep open Germany’s borders at the height of the 2015 refugee crisis as the “worst decision by any leader in modern political history”.
During New Year’s Eve celebrations in Cologne in 2016, scores of women were sexually assaulted and mugged by large groups of men. Police said the suspects were largely of north African origin and most had recently migrated to Germany.
For Berlin’s most recent New Year’s Eve festivities, a “women only” zone was set up.