Renzi last night told reporters in Rome he would "obviously" resign as leader of the Democratic Party. The country faces deep uncertainty as the rival parties try to convince Sergio Mattarella, the President, that they each have a mandate to form the new administration.
"We're like Christopher Columbus, sailing into the open sea without any idea where we're going," said Professor Giovanni Orsina, a political analyst from Luiss University in Rome. "Anything could happen."
Di Maio, a 31-year-old university dropout and former football stadium steward, said his party "feels the responsibility to form a government. This election was a triumph for the Five-Star Movement. We are the winners. More than half of voters in some regions have voted for us."
He said the party's strong performance meant that it "represents the whole nation, from Val D'Aosta (a northern region bordering France) to Sicily. The others can't say that." The party has historically said it would never enter into a coalition, although Di Maio said he would be "open to discussion with all political actors".
But Salvini was insistent that he should be the country's next prime minister.
The former journalist, who has pledged to deport hundreds of thousands of migrants back to their home countries, said he had "the right and the duty" to form a government after his party quadrupled its share of the vote compared with how it performed at the last election in 2013. "Italians have chosen to take back control of the country from the insecurity and precariousness put in place by Renzi," he said.
Salvini dismissed speculation that he would forge an alliance with the Five-Star Movement to form a government. He said he was implacably opposed to messy "minestrone soup" coalitions.
The big losers from the election were Renzi, whose party performed woefully, and Berlusconi, who after 25 years in politics may finally be finished. His party took 14 per cent of the vote.
"One never knows, but it seems to me that it will be hard for him to come back from this. For the right, Berlusconi is the past, Salvini is the future," said Orsina.
The League dominated the north and the Five-Star Movement swept the south.
In the case of prolonged deadlock, Mattarella could leave in place the centre-left government of Paolo Gentiloni, the Prime Minister. This would allow time to set up a temporary government to reform the electoral law and organise new elections.