The pair are vying to lead the country out of weeks of political deadlock that has emerged from the March 4 general election.
The third round of consultations centres on Di Maio's refusal to deal with Berlusconi, who the M5S sees as a symbol of political corruption, and the 81-year-old media magnate's distaste for the "anti-democratic" M5S.
And after meeting the Senate speaker on Wednesday afternoon Di Maio dug his heels in, calling Salvini's right-wing grouping "an electoral gimmick" and demanding that he come to the negotiating table alone.
"I expect a definitive response (from Salvini) by the end of the week," Di Maio told reporters.
"The country can't wait any longer."
Di Maio wants to create a German-style "government contract" with the League.
"The only forces capable of signing this contract and forming a government in these consultations are the M5S and the League," he added.
Alberti Casellati is an ally of former prime minister Berlusconi, and her election as the first ever female Senate speaker was part of a pact that aimed to smooth the path to an alliance between the M5S and the League.
They have been battling over who should lead the government since the M5S became Italy's largest single party with just under 33 percent of the vote and the right picked up 37 percent.
Despite Di Maio's pressure, Salvini has refused to break up the grouping that won the most number of seats in the parliament and given him a chance of becoming prime minister.
"I don't see respect for the people's vote. The one that came second dictating the rules to the one that came first," Salvini said.
Di Maio's ultimatum was designed to put pressure on Salvini, who is eyeing elections on April 29 in the northeastern region of Friuli Venezia Giulia, where a League candidate backed by Forza Italia is favourite to win.
It also opened the door to potential future talks with centre-left Democratic Party (PD), who are not involved in this round of consultations after their coalition came third and subsequently refused to deal with either the right or M5S.
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