President Sergio Mattarella's spokesman said he had asked Draghi, the former head of the European Central Bank, to meet with him for talks on Wednesday, after ruling parties failed to agree on a new government.
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The announcement came after Italy's ruling parties missed a deadline to reach an agreement on Tuesday, meaning talks on potentially forming a new government had failed.
“At present, there remain differences, in light of which I have not recorded a unanimous willingness to give life to a majority,” said House Speaker Roberto Fico, after meeting with President Sergio Mattarella.
Italy is currently without a prime minister amid a political crisis which has deepened since Conte resigned last week.
Mattarella had given the ruling coalition parties until Tuesday to patch things up with former premier Matteo Renzi's Italia Viva party, which sparked the crisis by withdrawing support.
But talks failed, and the president said he was left with only two viable options.
He ruled out snap elections because of the pandemic, and instead said he would help form a “high-profile government that should not identify itself with any political formula”.
Mattarella has stressed the urgency of creating a stable government to manage the pandemic, which hit Italy first among European nations and has been devastating.
Alongside the ever-mounting death toll, the economy shrank 8.9 percent in 2020 – the biggest contraction since the end of World War II.
Italy's La Stampa newspaper also reported on Sunday that Mattarella was considering Draghi for the prime ministerial role.
However, Mattarella's office promptly denied this, saying there had been no contact between them.
So far, there has been no comment from Draghi, who hasn't been seen much in the public eye since 2019.
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Conte had drawn up a 220-billion-euro ($240 billion) recovery plan using the EU funds, but Renzi accused him of using it for vote-winning handouts, rather than addressing long-term structural issues.
The lack of political leadership in recent weeks had sparked concerns about whether Rome could meet the April deadline to submit its spending plans to Brussels.
But Draghi, dubbed “Super Mario”, has long been cited by political watchers as the man to see Italy through the coming months.
“Thank you president!” tweeted the EU's economy commissioner, former Italian prime minister Paolo Gentiloni, after Mattarella announced his plans.
Lorenzo Castellani, a political expert at Rome's Luiss University, said he believed a Draghi-led government would be highly technocratic.
“The government programme will be 99 percent occupied by the pandemic and the recovery fund,” he told AFP, adding that it would likely find support among lawmakers.