Mattarella has already held two rounds of talks with party leaders which failed to end the stalemate while two further efforts at mediation carried out by parliamentary speakers also rapidly hit a brick wall.
A presidential palace official said on Thursday the president would see party representatives on Monday before deciding his next step. He has few options left at his disposal as calls grow for a swift return to the polls.
A national election on March 4 saw a center-right alliance led by the anti-immigrant League winning the most seats and the anti-establishment 5-Star Movement emerging as the biggest single party. The center-left Democratic Party (PD) came third.
A matrix of criss-crossing vetoes has so far prevented the parties from agreeing to a coalition deal, with friction and frustration growing by the day.
A source in the president's office told Reuters on Wednesday the head of state would not call a re-vote in June, ahead of summer holidays, preferring instead to try to find a stopgap government that would put together a 2019 budget.
If party leaders fail to sign up to such an administration, which would almost certainly be led by a non-political figure, then a new vote would be held in the autumn - probably October.
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