Far-right Italian activists and politicians, including the great-grandson of Benito Mussolini, have accused Facebook of “discrimination” after their accounts were apparently suspended.

“I find it unacceptable that Facebook has closed my personal profile just because my surname is Mussolini,” said the fascist dictator’s great-grandson Caio Giulio Cesare Mussolini on Monday, as he threatened legal action against the social network.

Caio Mussolini announced at the weekend that he was competing in the European elections in May as a candidate for the extreme rightwing Brothers of Italy, making him the third descendant of the dictator to enter Italy’s political arena.

Benito Mussolini bids Adolf Hitler farewell after their meeting in Florence in 1940. Photograph: Alamy

His second cousin Alessandra Mussolini is already a member of the European parliament and is likely to run again in May. Her sister Rachele is a city councillor in Rome.

Rachele Mussolini said: “Caio, like all Mussolinis, found himself being persecuted by [Mark] Zuckerberg’s thought police.

“I find this to be shameful, undemocratic and politically incorrect. I am indignant and embittered by the discriminatory attitude Facebook continues to adopt towards members of my family, as well as towards me.”

In an interview with the Italian newspaper il Fatto Quotidiano, Caio Mussolini, 51, described himself as “a post-fascist who refers to those values in a non-ideological way”.

He was a naval officer for 15 years, then an executive for Italy’s largest defence contractor, Finmeccanica before turning to politics.

The neo-fascist party CasaPound claimed on Tuesday that its leaders’ Facebook accounts had also been shut down by the company.

“Facebook has begun to systematically delete the personal accounts of the major representatives of CasaPound, just four days after the announcement that we will compete in the European elections on 26 May with one of our candidates,” the group wrote in a statement.

Both Caio Mussolini and CasaPound’s Facebook profiles later appeared to have been reactivated. Facebook did not immediately respond to a request for comment.

Last week, hundreds of CasaPound activists took to the streets of a Rome suburb in a violent protest against 70 Roma people, including 33 children and 22 women, who were to be temporarily transferred to a reception centre in the area.

In a video published by la Repubblica, protesters were shown trampling on food destined for the Roma, and someone could be heard shouting: “They must die of hunger.”

CasaPound has more than 275,000 followers. Its secretary, Simone Di Stefano, ran for prime minister in the previous general election. In a 2011 interview with the Guardian, he described Mussolini’s brand of fascism as “our point of reference, a vision of the state and the economy, and the concept of sacrifice”.