Financial markets have calmed amid increasing signs that Italy may avoid imminent elections after the president gave two populist parties time to figure out whether they can agree on an alternative to an anti-euro economy minister.
The continent's euroskeptic politicians cheered the birth of the new government coalition of the 5-Star Movement and the right-wing League party.
Investors, wary over the political impasse and the possibility that it might force new elections, sent Italian stocks plummeting in recent days.
Political neophyte Giuseppe Conte, who skipped teaching a class at the University of Florence to return to Rome, was summoned to meet Mattarella at the presidential palace Thursday night.
The key economy ministry went to a mainstream economist, Giovanni Tria, who is close to the center-right Forza Italia party of ex-Premier Silvio Berlusconi.
Political crises in Italy are nothing new, but the latest political dysfunction there is rippling right across the global economy.
Republic Day commemorates the day, June 2, 1946, when Italians voted in a referendum to abolish the monarchy in favor of a republic, Italy's first. The 5-Stars received 32 percent of the vote, making the movement the largest single party in the Italian Parliament.
In a Facebook post, Di Maio gushed: "There are a lot of us, and we're ready to launch a government of change to improve the quality of life for all Italians".
The ceremony sets the stage for the formal handing over of the government later Friday.
Economic analyst Lorenzo Codogno said any possible political government would likely mean tweaks to the coalition agreement, including dropping Savona as economy minister.
After the swearing-in, Salvini told reporters his first order of business would be to "reduce the arrivals and increase the expulsions" of migrants, as well as the costs associated with their care.More news: West Indies thrash ICC World XI by 72 runs
"It's the celebration for all of us, of our republic", he said.
Yet migrant arrivals to Italy actually plunged in the previous year under the center-left Democratic Party, which signed controversial deals with Libya to beef up coastal patrols and prevent migrants from setting out in smugglers' boats across the Mediterranean Sea.
But Salvini also insisted that the proposed Cabinet be accepted, Savona included.
The 5-Stars and League together won a narrow majority in the March 4 election.
The new government delighted leaders of an increasingly bolder far-right in European politics.
"It's a victory of democracy over intimidation and threats from the European Union", said Le Pen, who shares the League's firm anti-immigrant stance. Nigel Farage, a British force behind the successful Brexit movement, advised Italy's populists to "stay strong or the bully boys will be after you".
It was a reference to European Union officials, who have made clear in recent days their concerns - in occasionally undiplomatic terms - about the euroskeptic direction of Europe's third-largest economy.
But on Thursday EU chief Jean-Claude Juncker warned against blaming the EU for all of Italy's problems.
Italy's new populist leaders promised to get to work creating jobs and curbing illegal migration as they made their first outing at Saturday's symbolically-rich anniversary commemorations for the founding of the Italian republic. Seriousness", he said. "We will help them, as we always did.
League leader Matteo Salvini, meanwhile, had a series of rallies in northern Italy.
The European Union's executive says it is "committed to work with the new Italian government to tackle the many common challenges that Italy and Europe are facing". But he said he refused to accept that all of Italy's ills can be blamed on the EU.