Mattarella said a parliamentary majority could be found based on the members of Conte’s previous coalition and summoned the speaker of the lower house, Roberto Fico, to open more detailed talks running through Tuesday.
Italy’s government has been in turmoil ever since former premier Matteo Renzi withdrew his Italia Viva party earlier this month, a move that forced Conte to step down last week.
The prime minister has stayed on in a caretaker position while dealing with the COVID-19 pandemic, which has left more than 87,000 people dead in Italy and triggered a deep recession.
Earlier on Friday, the largest party in parliament, the Five Star Movement (M5S), lobbied for Conte’s return while signalling it is willing to patch up the alliance with Renzi.
“For the Five Star Movement, the only person capable of leading the country with seriousness and efficiency through this particularly complex phase is Giuseppe Conte,” M5S leader Vito Crimi told reporters.
The centre-left Democratic Party (PD), the other main party in the coalition, has also so far backed Conte.
Mattarella has been meeting since Wednesday with all ruling parties to establish whether Conte has enough support to lead a stronger government, or if another prime minister should be chosen.
“The perspective has emerged of a political majority based on the groups that supported the previous government,” the president said on Friday, adding that it still needed to be “verified”.
Renzi withdrew his party after weeks of criticising Conte’s handling of the coronavirus pandemic, particularly how to spend European Union recovery funds.
His withdrawal deprived Conte of his majority in the Senate, the upper parliamentary chamber, although opinion polls suggest the premier is still Italy’s top choice for prime minister.
If Mattarella does eventually decide to grant Conte a new opportunity, the premier will seek to repair relations with Renzi and his party, while continuing his search for pro-European, centrist and unaffiliated lawmakers, especially in the Senate.