ROME (Reuters) - Alessandra Mussolini, granddaughter of Italy´s wartime Fascist dictator, said on Thursday she was quitting the right- wing National Alliance, in the week that the party edged further to center of Italian politics.

The leaders of the party, Italy´s third-largest, immediately went into a huddle with the 40-year-old Mussolini to try to convince her to change her mind.

Mussolini has long been at odds with party leader, Deputy Prime Minister Gianfranco Fini, who has shifted the National Alliance more to the center and just completed a controversial trip to Israel where he denounced Italy´s Fascist past.

There, he condemned Benito Mussolini for the racial laws that led to the deportation and death of some 6,000 Italian Jews in Nazi camps and said he had been mistaken in 1994 when he praised the dictator as a great statesman.

Alessandra Mussolini was quoted as telling the Italian news agency Ansa that she had decided to quit the party because it appeared it was "incompatible with my last name."

She said she would remain a member of the lower house Chamber of Deputies and join a group of non-aligned lawmakers.

Last year Alessandra Mussolini challenged Fini for the leadership of Italy´s biggest right-wing party, saying it needed "a big shaking up." She later withdrew her challenge.

The National Alliance is the successor to the neo-Fascist Italian Social Movement party, which was disbanded in 1994 to form the new party.

Alessandra Mussolini rocketed to political prominence in 1992 on the back of Italy´s most famous last names -- that of her dictator grandfather and of her film-star aunt, Sofia Loren.

The once-aspiring actress and model has often said that she is fiercely proud to be a descendant of Benito Mussolini, who ruled Italy with an iron fist for over two decades.

A magnet for nostalgic Italians, the blonde, dark-eyed Mussolini built her political career on vows to restore her grandfather´s ideals of hard work and pride to a nation whose reputation was hurt by political corruption scandals.

On her first day in parliament, Mussolini asked to sit in her grandfather´s chair.

"My grandfather was a great man, I have a bust of him in my bedroom. What I want to do is bring the honesty of his character into parliament," she said during her 1992 election campaign.

During that campaign nostalgic Italians flocked to her, bearing dog- eared pictures of "Il Duce," and giving her the Roman salute, one of her grandfather´s trademarks.

Benito Mussolini was overthrown by his own followers in 1943. The Germans freed him from jail and set him up at the head of a puppet regime in northern Italy until the end of the war, when he was executed by partisans. (Additional reporting by Antonella Ciancio) (© Reuters 2003 11/27/03)