Italian Catholic and Jewish leaders on Tuesday condemned as outrageous an episode in which right-wing extremists put a flag with a swastika on a coffin outside a church after a religious funeral and gave Nazi salutes.

Rome's Catholic archdiocese said in a statement that priests at the parish of St. Lucy in a central Rome neighbourhood, including the one who presided at the funeral rite, had no idea of what would happen outside the church on Monday.

Pictures on the internet showed the coffin bearing the body of Alessia Augello, a former member of the right-wing extremist group Forza Nuova, covered by the flag.

The diocese statement called the flag "a horrendous symbol that cannot be reconciled with Christianity" and said the episode was an offensive example of "ideological exploitation" of a religious service.

Police said they were investigating the incident as a possible hate crime.

Rome's Jewish community expressed outrage that such events could still happen more than seven decades after the end of the Second World War and the fall of Italy's fascist dictatorship.

"It is unacceptable that a flag with a swastika can still be shown in public in this day and age, especially in a city that saw the deportation of its Jews by the Nazis and their fascist collaborators," the statement said.

After a raid on Rome's Jewish neighbourhood on October 16, 1943, more than 1,000 of the capital's Jews were deported, most to the Auschwitz death camp in Nazi-occupied Poland. Only 16 returned.

The Jewish community statement on Tuesday said the funeral incident was "even more outrageous because it took place in front of a church."

A similar incident took place outside another Rome church in March of last year.