Saturday's agreement between the right-wing coalition and the anti-establishment Five Star Movement (M5S) will allow them to begin consultations with Italian President Sergio Mattarella over who will lead the new government.
In an interview on Sunday in the Corriere della Sera, M5S leader Luigi Di Maio said "the match" to see who will win power was in no way related to the battle of parliament speakers.
"But starting today, those who want to work for the people know that there is a reliable and serious force who will talk with everyone and advance together for the good of the country," he added.
He claims M5S' right to lead the country after it secured 32.6 percent of votes in the lower house, the largest of any single party, after campaigning to cut taxes, amend pension reforms and improve youth unemployment.
However, a right-wing coalition led by Matteo Salvini, which includes former prime minister Silvio Berlusconi's Forza Italia party, together secured 37 percent.
"The next head of government needs to be proposed by the right," Salvini declared on Twitter on Sunday.
His priorities include the abolition of pension reforms and lowering taxes as well as a revision of European treaties and the eviction of illegal immigrants.
On Saturday, an agreement between the two sides saw a member of the Five Star Movement, Roberto Fico, elected speaker of the lower house, the Chamber of Deputies.
In return, Elisabetta Alberti Casellati, a Forza Italia member, was voted head of the upper house, the Senate.
Prime Minister Paolo Gentiloni, who led Italy's previous centre-left government, meanwhile, officially tendered his resignation.
He will continue to manage the day-to-day affairs of the government until a new one was formed, the presidency said in a statement.