Di Maio's Five Star Movement (M5S) won the largest share of the vote for any single political party from the March 4th general election with nearly 33 percent. He immediately claimed victory in the aftermath despite a hung parliament.
"Italy sent a strong signal on March 4th... and that gave 32.5 percent to the M5S," the 31-year-old told a press conference on Tuesday.
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He is vying with the four-party right-wing coalition that conquered 37 percent of the vote for the chance to lead the next government.
To do so he has to convince the far-right League or the centre-left Democratic Party (PD) to form a coalition. But neither League leader Matteo Salvini nor the PD have budged since the vote.
Salvini has repeatedly claimed his own group's right to try to form a government. Interim PD leader Maurizio Martina, who took over from ex-prime minister Matteo Renzi, has followed his former boss's insistence that they remain in opposition.
"I say to the M5S and League: the people voted for you to govern. Now do it," Martina said after being named party leader on Monday.
Di Maio asked rival parties to bring him "proposals" that could help create a government. But he said that he would not change his party's manifesto pledges nor accept a different ministerial team from the one he proposed before the election.
"I have not seen yet a single proposal," he said. "If the other political forces have not understood the signal that was sent by the Italians, maybe they need a stronger signal," he added.
"Maybe they are asking to return to the polls."