ROME (Reuters) - Italy's 5-Star Movement chose investigative television journalist Milena Gabanelli as its candidate for the presidency following an online vote by supporters, the anti-establishment party said on Tuesday.

The election of a successor to President Giorgio Napolitano, whose term ends on May 15, is a vital step toward resolving a stalemate after February's inconclusive election left no party able to form a government.

The next president's first task will be to find a way out of the deadlock, either by persuading the parties to come to an accord or by calling new elections. The choice of the head of state has caused fierce political wrangling.

The two houses of parliament, along with delegates from the regions, will start voting on Thursday, a process that may involve several rounds. No clear favorite has emerged.

The nomination of Gabanelli, a well-respected journalist from state broadcaster RAI but a complete outsider to traditional politics, is unlikely to shift the battle between the center-left alliance led by Pier Luigi Bersani and Silvio Berlusconi's center-right bloc.

However it ends speculation that the 5-Star Movement could back former prime minister Romano Prodi, who is strongly opposed by Berlusconi but supported by elements of the center-left.

In 5-Star's online consultation of its members Prodi came eighth on a short-list of 10 candidates selected in a preliminary ballot.

Prodi, a former president of the European Commission, is among the names most frequently mooted in the media as a possible president but Berlusconi has rejected supporting one of his oldest political rivals as head of state.

The other name most often spoken of is former prime minister Giuliano Amato, who is well-known outside Italy for his handling of a financial crisis in 1992 but is handicapped by his image as a member of the traditional political elite, now widely distrusted in Italy.

As well as a ceremonial function, the head of state has an important, broadly defined political role in overseeing government, as Napolitano demonstrated during the 2011 financial crisis when he appointed Mario Monti to lead a technocrat administration.

The leader of the 5-Star Movement, ex-comic Beppe Grillo, was prevented from standing because a manslaughter conviction following a traffic accident in 1981 makes him ineligible under party rules.

(Reporting by James Mackenzie)