Conte, a political novice, was finally sworn in on Friday as the head of a government of ministers from the anti-establishment Five Star Movement and the far-right League, ending months of uncertainty since elections in March.
But Conte was a compromise candidate between Five Star leader Luigi Di Maio and the League's Matteo Salvini -- both of whom are now his deputy prime ministers -- and he will have to walk a delicate line to push through the
anti-austerity and pro-security promises their populist parties campaigned on.
The 53-year-old academic also inherited a daunting list of issues from his predecessor Paolo Gentiloni, including the financial travails of companies such as Ilva and Alitalia, a Group of Seven summit in Canada and a key EU
summit at the end of the month, as well as the thorny question of immigration.
Immigration is the bugbear of Conte's interior minister, Salvini, the 45-year-old leader of the anti-immigrant, anti-Islam League.
Salvini announced on Friday that he would visit Sicily to see the situation for himself at one of the main landing points for refugees fleeing war, persecution and famine across North Africa and the Middle East.
"The good times for illegals is over -- get ready to pack your bags," Salvini said at a rally in Italy's north on Saturday, adding however that he wants to economically assist migrants' countries of origin.
His comments come after more than 150 migrants, including nine children, disembarked from a rescue ship late Friday in Sicily.
'From today, the state is us'
Conte attended a military parade alongside President Sergio Mattarella on Saturday, marking Republic Day for the foundation of the Italian Republic in 1946.
However the new prime minister has issued few public statements since being appointed.
On Saturday he did post on Facebook that he had spoken with German Chancellor Angela Merkel and French President Emmanuel Macron and would meet the two leaders at the G7 summit, where he will be a "spokesman for the interests of Italian citizens".
Conte has also opted to keep the country's intelligence services under his personal control.
Deputy premier Di Maio, who is serving as economic development minister, also took to Facebook, calling for "entrepreneurs to be left alone".
"Employers and employees in Italy must not be enemies," he said, promising "I will not disappoint you".
On Saturday evening Five Star held a rally in the centre of Rome with thousands of supporters and all its ministers to celebrate "the government of change".
Di Maio told the crowd that "from today, the state is us".
Five Star's founder, former comic Beppe Grillo, rang a bell in front of the crowd, saying the sound "marks the fracture between a world that is going away and a new one that is arriving".
EU and the eurosceptics
The world will be carefully watching power relations between Conte and his two influential deputies -- particularly the European Union, given the eurosceptic government is the first populist coalition in a founding EU member.
EU Commission chief Jean-Claude Juncker called on Saturday for Conte's new government to be treated with respect, having earlier sparked controversy by telling Italians to work harder and stop blaming the EU for the country's problems.
"We should show respect towards Italy," Juncker said in an interview with the German press group Funke Mediengruppe.
Juncker said Italy must not suffer the same fate as thrice-bailed out Greece whose dignity was "trodden under foot" by its creditors when left-wing Prime Minister Alexis Tsipras took office in 2015.
"That must not happen again in the present case with Italy," Juncker said. "Italians have a clear understanding of what is good for their country. They will sort it out."