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.
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.