The military parade, which Conte attended alongside President Sergio Mattarella, marked Republic Day for the foundation of the Italian Republic in 1946.
Conte was finally sworn in on Friday afternoon at the head of an anti-establishment and eurosceptic government, ending months of uncertainty since elections in March.
The 53-year-old academic heads a government of ministers from the anti-establishment Five Star Movement (M5S) and the far-right League Party, the first populist coalition in a founding EU member.
A political novice, he inherits 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, who announced Friday 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 immigration question remains a hot-button issue, even if the number of new arrivals has fallen,” said Salvini, an ally of French far-right leader Marine Le Pen.
“I'll be in Sicily on Sunday. The situation is now calm but only because of the rough seas.”
More than 150 migrants, including nine children, disembarked from a rescue ship late Friday in Sicily.
Salvini had said after being sworn in that he would ask his ministry's experts “how to reduce the number of arriving migrants and increase the number of expulsions.”
As premier, Conte will be responsible for pushing through the anti-austerity and pro-security promises that the two populist parties campaigned on.
Salvini and Economic Development Minister Luigi Di Maio, head of the M5S, also serve as deputy premiers to Conte.
While Conte has hardly made any public statements since being appointed, both Di Maio and Salvini have been much more outspoken.
EU Commission chief Jean-Claude Juncker called Saturday for Conte's new eurosceptic Italian government to be treated with respect, having earlier told 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.”