"This is the moment for bravery and determination. The courage to build a better Italy. The determination to pursue this objective without being deterred by obstacles," Conte told reporters after meeting Mattarella.
"It is a very delicate phase for the country. We must leave swiftly leave behind the uncertainty triggered by the political crisis," he added.
The government between the centre-left Democratic Party (PD) and the anti-establishment 5-Star Movement which Mattarella had asked him to form must "immediately" focus on a budget that protects savings and "creates solid prospects for growth and for social development," he said.
Looking ahead to November, when the new European Commission takes office, Italy must "make up for lost time," Conte underlined.
"This will enable Italy, a founder member of the EU to play a leading role in the bloc - as it deserves to," Conte said.
Conte has conditionally accepted Mattarella's mandate and is expected to be given a few days for political consultations to ensure a PD-5-Star government would have a working majority in parliament.
A little-known law professor with no political affiliation, he was chosen last year as compromise prime minister to lead the coalition government between 5-Star and the far-right League party. The government fell earlier this month when League leader Matteo Salvini withdrew his party from the coalition, hoping to trigger and win a snap election.
( With inputs from IANS )