French actress Fanny Ardant is being sued by the son of a former Italian policeman killed by the extremist Red Brigades group in the 1970s.
Ardant is reportedly thinking of cancelling her trip to Venice
The actress sparked a controversy when she told an Italian magazine she considered the jailed founder of the Red Brigades her "hero".
She has since apologised for causing offence but the policeman's son, Piero Mazzola, has said that is not enough.
In Italy it is illegal to praise someone who has committed a crime.
Ardant said she admired the founder of the Red Brigades group, Renato Curcio, because he had never abandoned his leftist ideals, adding she "considered the Red Brigades phenomenon to be very moving and passionate".
'Praising a murderer'
The Red Brigades murdered Christian Democrat leader Aldo Moro in 1978.
Ardant later said: "My words have caused suffering to those who have suffered and for that I ask for forgiveness."
Mr Mazzola, a lawyer whose father was shot along with a colleague near Venice in 1974, said her apologies were not enough.
"Curcio was convicted for killing my father, among other crimes. So, together with my family, I have filed legal proceedings against Ardant because she is praising a murderer," Mr Mazzola told Reuters news agency.
"I just can't see how killing people can be called heroism," he said. "She may see the Red Brigades as passionate while sipping champagne in Paris, but for us it's very different."
Ardant is due to attend this week's Venice Film Festival as the lead actress in the Italian film L'Ora di Punta.
But the president of Italy's Veneto region, Giancarlo Galan, has asked her not to come to the festival and Italian media reports that Ardant may cancel her trip for fear of overshadowing the film's release.
The Marxist Red Brigades group, whose aim was to overthrow capitalist Italy, attacked government and business targets in the 1970s and early 1980s.
It was largely disbanded in the 1980s but an offshoot of the group, which calls itself the Red Brigades-Communist Combatant Party, killed an Italian government consultant, Massimo D'Antona, in1999.
The group also assassinated another government adviser, Marco Biagi, in 2002.