Mattarella has already held two rounds of talks which failed to end the stalemate while two further efforts at mediation carried out by parliamentary speakers also hit a brick wall.
"After two months, the initial positions of the parties have not changed. No prospect has emerged for a government," the head of state's office said in a statement, adding that the president wanted to hear if party leaders had any other ideas.
Mattarella's options are rapidly dwindling and the possibility of a return to the polls sometime between the coming autumn and next spring looks increasingly likely.
A national election on March 4 saw a centre-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 centre-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.
Underscoring the sense of paralysis, the PD was due to decide later on Thursday whether to open formal negotiations with 5-Star. However, Mattarella did not wait for their decision before announcing Monday's meetings - an acknowledgement that the deeply divided party will be unable to agree to such a deal.
Having come to the same conclusion, the leader of the 5-Star this week called for an immediate revote in June, but a source in the president's office told Reuters on Wednesday that the head of state would reject this demand.
Instead, Mattarella wants to put together a stopgap government to draw up a 2019 budget that has to be approved by the end of December.
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.
The last four Italian prime ministers took office thanks to backroom deals rather than ballot-box victories and repeated efforts to reform the electoral law that would allow for the swift formation of a government have failed to come up with a winning formula.
While 5-Star is pushing for an immediate re-vote, other parties have suggested working together to devise a new election system. However, winning wide backing for such a pact in the current political climate looks highly unlikely.
While Italy's day-to-day administration is being overseen by caretaker prime minister Paolo Gentiloni, latest economic forecasts from the European Commission have underlined the need for a fully empowered government ready to undertake reform.
The forecasts showed that the Italian economy was set to grow 1.5 percent this year and just 1.2 percent next -- the lowest amongst the European Union's 27 member states.