Five Star Movement (M5S) leader Luigi Di Maio and head of the anti-migrant League party Matteo Salvini will each meet with President Sergio Mattarella on Thursday afternoon to make their case for leadership following the stalemate delivered by March's general election.
The right-wing coalition led by the League that also includes former Prime Minister Silvio Berlusconi's Forza Italia party won 37 percent of the vote. M5S got the biggest share of any single party with just under 33 percent.
M5S leader Luigi Di Maio made a play for power in the lead up to the consultations, saying he would be willing to work with either the League or the centre-left Democratic Party (PD), on the condition that he take the top spot.
But Di Maio staunchly ruled out working with Salvini's coalition partner Berlusconi, a fierce rival of the M5S.
"Salvini needs to choose between revolution and the restoration. Whether to leave Berlusconi and change Italy or whether to stay with him and not change anything," said Di Maio.
The second day of the two-day consultation process began at 0800 GMT on Thursday with the Democratic Party, whose centre-left coalition came third with just under 23 percent of the vote.
They were to be followed by Berlusconi and Forza Italia at 0900 GMT and Salvini an hour later. Di Maio will be the last leader to speak with Mattarella at 1430 GMT.
After his consultations the president will take some time to decide who, if anyone, can command enough seats to form a government or whether a fresh round of consultations is necessary.
Finding a solution this week will be tricky given how far any group is from a majority in either the lower house Chamber or upper house Senate.
The PD has refused to work with either the right or M5S despite having enough seats to form a government with either.
"Everyone is stuck in their positions and if nobody moves, we will vote again," Salvini told reporters Thursday morning.