The euro rallied against the dollar at the end of a day of drama that saw the prospect of a populist government determined to take on Europe recede for now.
He would be a calming choice for the financial markets, who were spooked by Savona's criticism of the euro and German economic policy.
His veto of Savona infuriated the leaders of those parties, who on Sunday evening were talking not about presenting fresh proposals to Mattarella, but rather calling for new elections.
The constitution also gives the president the power to dissolve parliament, a deterrent force which has played a part in numerous prior political crises in Italy - a country which has had 64 governments since 1946.
Shortly afterwards, he summoned former International Monetary Fund (IMF) senior official Carlo Cottarelli for a Monday morning meeting - an indication he may be considering asking him to head a government of unelected technocrats.
However, the Prime Minister designate, Giuseppe Conte, yesterday said he had "returned the mandate" to form a government offered by Mattarella after the President vetoed the appointment of a veteran eurosceptic as economy minister.
"The adhesion to the euro is a choice of fundamental importance for the perspectives of our country and our youth", Mattarella said.
"We need to keep cool".
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The centre-right Forza Italia party and the centre-left Democratic Party (PD) both denounced calls for impeachment.
"They've replaced a government with a majority with one that won't obtain one", said Di Maio.
Conte, 53, is working on a list of ministers to propose to Sergio Mattarella, 76, the head of state whose task it is to name the government team.
Last week, it looked as if Italy was finally about to get a new government after nearly three months of political deadlock following inconclusive elections back in March.
Luigi Di Maio of the 5-Star Movement attends a news conference in Rome. "Everything was set, and I, too, was ready to deal with immigration and security, but someone today said NO".
"Italians decide their own government", Moscovici said. Anger? Lots. Fear? Zero.
After markets had closed on Friday, Moody's said it may downgrade the country's sovereign debt rating because of the risk that the would-be government would weaken public finances and roll back a 2011 pension reform. I'm not giving up Friends, I'm counting on You.
The Five Star and League movements have said they will support earlier elections, and electoral polls indicate they would garner even more votes the second time around.
Demanding an immediate ballot, Salvini told followers on Facebook: "It won't be an election, it will be a referendum between Italy and those on the outside who want us to be a servile, enslaved nation on our knees".