The stalemate puts the spotlight on Mattarella, who has the power to name a prime minister, but it is still unclear whether rivals can find common ground for a coalition government or whether another vote will be needed.
Luigi Di Maio's anti-establishment Five Star Movement (M5S) garnered more than 32 percent of the vote in the March 4th poll but the anti-immigration League of Matteo Salvini leads a coalition that got 37 percent of the ballot.
The parliament is divided between the right-wing coalition, the M5S and the centre-left Democratic Party.
Late last month, the right-wing coalition and the M5S cobbled a deal on the respective positions of speaker for both the lower and upper houses of parliament but they have not come to any pact on forming a government.
Far-right leader Salvini said on Thursday that his aim was for his party to take power.
"We are open to dialogue with everybody but we are not subordinate to anyone given that the centre-right coalition got the most votes," he said on Facebook.
Di Maio meanwhile stressed that his M5S was the party with the most seats.
"The biggest challenge facing us however is forming a government while respecting the popular will," he said.
Mattarella will on Wednesday hold preliminary talks with the speakers from the two houses of parliament as well as with his predecessor Giorgio Napolitano before launching further discussions with the parties.
The consultations could last weeks.
The left has so far refused to enter into coalition talks with either the M5S or the right-wing coalition.