ROME (Reuters) - President Sergio Mattarella may appoint a neutral institutional figure to mediate between Italian political parties, which have failed to break a deadlock since inconclusive elections last month, a source close to the president said.

Italian President Sergio Mattarella leaves after speaking to the media during the second day of consultations at the Quirinal Palace in Rome, Italy, April 5, 2018. REUTERS/Alessandro Bianchi

Mattarella will hold formal consultations with all the parties on Thursday and Friday, the second round of talks since the March 4 vote produced a hung parliament.

The anti-establishment 5-Star emerged as by far the largest single party, while a conservative coalition of smaller groups, led by the far-right League, has the most seats in parliament but not enough for an absolute majority.

If, as expected, the parties maintain their irreconcilable positions during their meetings with Mattarella, his next move may be to appoint someone else to hold more flexible, informal talks aimed at brokering a deal, the source said.

A so-called “exploratory mandate” has been used before at times of stalemate, and whoever is given the task would not be expected to form a government themselves.

The president could give the job to anyone with a high profile institutional role, such as one of the speakers of the two houses of parliament or a judge from the constitutional court.

Political sources say the impasse is unlikely to be broken before local elections later this month in the small regions of Molise in the south, and Friuli Venezia Giulia in the north.

Both 5-Star and the League look unwilling to compromise while campaigning, with 5-Star hoping to win control of its first ever region in Molise and the League the hot favorite to win a clear victory in Friuli Venezia Giulia.

5-Star leader Luigi Di Maio has called for a German-style coalition policy agreement with either the League or the centre-left Democratic Party (PD), which was a big loser at the election, but his proposal has so far been rejected by both.

The PD says it wants to go into opposition, while League leader Matteo Salvini has refused to break with his coalition ally Silvio Berlusconi - a condition posed by Di Maio.

The 5-Star Movement, which bases its appeal on a promise to clean up politics, refuses to countenance a deal with the 81-year-old media billionaire who has a conviction for tax fraud and is on trial for bribing witnesses - a charge he denies.

If Mattarella, with the possible help of his appointed mediator, fails to break the impasse, he would have to call new elections, almost certainly in the autumn. But the source in his office said he was determined to avoid this.