RAI-1 state television said Tuesday that the MSI polled 14.4 percent of the vote compared with 14.1 percent for the ex-communist Democratic Party of the Left.
MSI candidates will be in mayoral runoff elections in both Rome and Naples, and the party's other candidates did well elsewhere in the country.
Alessandra Mussolini, the dictator's 30-year-old granddaughter, won about 30 percent of the Naples vote to force a runoff with a leftist candidate who
drew 48 percent.
The race in Rome was even closer, with the party's national leader, Gianfranco Fini, just a few percentage points behind another leftist-backed candidate.
Mussolini, a former actress, has not denied that identification with her grandfather brought her votes. "Il Duce" ruled from 1922 until he was ousted and slain in 1943.
Speaking to reporters after Sunday's election, Alessandra Mussolini emphasized that point and said the name "represents immortal values that cannot be erased."
The MSI platform stresses the need for public order, for controls on immigration and for the death penalty, outlawed since World War II, for certain crimes.
The party has 50 seats in the Italian parliament and consistently garnered about 6 percent of the national vote. However, it has long been shunned by the traditional parties.
Italy's postwar constitution bans the revival of the Fascist Party. But the City of Rome has allowed some Mussolini-era buildings to remain as well as an obelisk bearing the name "Duce," Mussolini's title as dictator.
Alessandra Mussolini often pays tribute to her grandfather, praising him for restoring pride in Italians. However, she has taken issue with his racial laws that foreshadowed the deportation of Jews to Nazi concentration camps.
In the Rome race, Fini worked hard at a mainstream approach and attributed much of his success to his showing in poorer areas of the capital, previously leftist strongholds. Campaign posters depicted him with a jacket slung over his shoulder in what newspapers described as an attempt at a "yuppie look."
While the MSI clearly has right-wing policies, it endorses the democratic process and does not condone violence or anti-racial or anti-Jewish stances. Mussolini and Fini both have made gestures of reconciliation with the small Jewish communities in Rome and Naples.