For the first time since the March 4 vote ended with a hung parliament, Mr Di Maio said he would pick a prime minister with League leader Matteo Salvini.
Until now, Mr Di Maio has insisted that he be the next premier.
“If the goal is to put into action an election platform and the obstacle is Luigi Di Maio as premier, then I say let’s choose a prime minister together,” Mr Di Maio said referring to the League during an interview on RAI state television.
The move came hours before a third and possibly final round of formal consultations with President Sergio Mattarella.
The M5S will meet the president at 10:00 am Rome time on Monday, with the League leading the center-right delegation to the presidential palace an hour later.
While Mr Di Maio conceded the prime minister’s office, he held his ground on insisting that Mr Salvini abandon his ally, former prime minister Silvio Berlusconi, who the M5S views as a symbol of political corruption.
“The ball is now in the center-right’s court,” Mr Di Maio added, saying he did not know if Mr Berlusconi would take “a step back”.
Mr Salvini, Mr Berlusconi and Giorgia Meloni - the leaders of the center-right alliance - met for more than two hours in the evening, and agreed to see each other again in the morning before their appointment with the president.
“For now the center-right remains united, but it’s not over yet,” a senior source in Mr Berlusconi’s party said after Sunday night’s talks.
Mr Salvini has repeatedly refused to break with Mr Berlusconi over the past two months.
If the alliance remains united this time, President Mattarella is expected to try to put forward a stopgap government to take Italy back to a vote later this year.
Mr Di Maio said if the M5S fails to come to an agreement with the League, he wants an election as soon as possible, as early as this summer.
The M5S will not support any government put together by Mr Mattarella, the M5S leader said.
Such a short-term government could only take office with full powers if it has the support of either the M5S or the League, and both parties have been hostile to the idea.
“A government put together by the president would not have the numbers (in parliament),” Mr Di Maio said.
“We cannot vote confidence in it and as far as I know, neither would the League.”
Mr Di Maio’s latest offer to the League followed Mr Salvini’s proposal on Friday for the formation of a stopgap government between the center-right and the M5S that would be tasked with writing a 2019 budget and preparing for a new election.
Mr Mattarella, who has the power to select prime ministers and dissolve parliament, has sought to avoid another vote by conducting meticulous and patient negotiations, but now a source familiar with the situation has said an election in September or October cannot be ruled out.
“I thought it would be difficult [to form a government], but I didn’t think it would be impossible,” Mr Di Maio said.