Initial talks with the country's president failed to provide a solution to the deadlock following March's inconclusive election.
But the leaders of the League, Forza Italia, and Brothers of Italy said on Sunday that they planned to present "a common front" in the next round of talks, set to take place next week. They met at Silvio Berlusconi's residence in Arcore near Milan in the north of the country.
Such a stance would likely freeze out the populist Five Star Movement, which emerged as the largest single party but has said it will not govern with Berlusconi. The 81-year-old Forza Italia leader has repeatedly criticized the newer party, which he has described as a "sect".
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The centre-right bloc won the most seats in the vote but fell short of the majority needed to govern.
The party leaders stressed in their statement the need for "a government that respects the will of the citizens as expressed in the March election", and said the responsibility of forming a government should "undoubtedly" fall to the centre-right.
Berlusconi's Forza Italia had a disappointing performance in the election, overtaken by Salvini's League as the dominant party in the centre-right group.
Since the results, Salvini has appeared keen to assert this dominance, and on Sunday issued a separate statement alongside the joint one.
In that statement, the League leader said he was open to all scenarios other than a deal with the Democratic Party (PD).
"This week I will continue to talk with others, starting with Di Maio," he said, adding that if he is able to form a government he would be "proud" to do so.
However, he also took to Twitter to criticize the Five Star leader, writing: "Di Maio talks of change and yet is open to the PD".
Meanwhile, Di Maio sniped at Salvini using his own preferred social media platform, saying in a Facebook post "I see that the League promised change but prefers to keep Berlusconi close and condemn itself to irrelevance."
He added that if Salvini changed his mind about ditching Berlusconi, he should "give us a call; we'll tell him if we're still available to work with him".