The president rejected the candidate for the Economy Ministry proposed by Italy's prime minister-designate candidate.
Italy's Prime Minister-designate Giuseppe Conte gave up on efforts to form a government on Sunday after the president apparently rejected his pick for the economy ministry, increasing the likelihood of another election this year.
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Conte, a little-known law professor with no political experience, took his list of ministers to President Sergio Mattarella in a bid to end a two-month political stalemate.
But the president rejected Conte's candidate to the Economy Ministry, the 81-year-old eurosceptic economist Paolo Savona.
Before Conte or Mattarella had finished their meeting, far-right League leader Matteo Salvini said that the only option now was to hold another election, probably later this year.
"In a democracy, if we are still in democracy, there's only one thing to do, let the Italians have their say," Salvini said in a fiery speech to supporters in central Italy.
Salvini and 5-Star leader Luigi Di Maio had met Mattarella informally on Sunday to try to find a solution. Mattarella is expected to speak soon about his decision.
"The problem is Savona," the coalition source said, explaining that the economist had not sufficiently softened some of his more eurosceptic positions.
On Sunday, Savona tried to allay concerns about his views in his first public statement on the matter. Savona has been a vocal critic of the euro and the European Union, but he has distinguished credentials, including as industry minister in the early 1990s.
"I want a different Europe, stronger, but more equal," Savona said in a statement.
Outgoing Economy Minister Pier Carlo Padoan said on Sunday that the problem was not Savona, but the coalition's economic plan, which is "clearly unsustainable".
Savona has had high-level experience at the Bank of Italy, in government as industry minister in 1993-94, and with employers' lobby Confindustria. But his critical stance on the euro has been the focus of concern.
In Sunday's statement Savona did not refer to his opinions on the euro, but more than 70 slides outlining a "plan B" for Italy's exit from the euro, co-authored by Savona in 2015 with a dozen others, circulated on social media.
If the president were to continue to veto Savona, the risk is that the deal holding together the two rival parties, which won the most parliamentary seats in the March vote, would fall apart, making another election this year likely.