Matteo Salvini, leader of the far-right League, the biggest party in the right-wing coalition that came first with 37 percent of the vote in Sunday's election but failed to win an overall majority, said his team was ready to govern.
"We have a programme, a team. If they call us, we'll start work tomorrow morning," he told reporters.
But Luigi Di Maio, leader of the anti-establishment Five Star Movement (M5S), declared his party "the winners", after obtaining alone nearly 33 percent of the vote, but M5S would also need to form alliances in parliament to gain a majority.
Matteo Renzi, who announced his resignation as Democratic Party (PD) leader on Monday after his centre-left coalition in the election slumped to third place on 23 percent, ruled out the prospect of a deal with either the Five Star Movement or the right-wing alliance.
In a Facebook post on Tuesday Renzi said he would not work with those who "have insulted us for years and who represent the opposite of our values".
"They've said that we're corrupt, mafiosi and that we have blood on our hands due to immigration. I don't believe that they've suddenly changed their minds," wrote the former prime minister.
"If anyone wants to support the right-wing or the Five Star Movement they should say so. I personally think it would be a glaring and tragic mistake," he added.
However, other leading voices in his party disagree and he now faces pressure to bring forward his resignation.
In an interview with Il Fatto Quotidiano daily, Michele Emiliano, governor of the Puglia region and a leading PD member, berated Renzi for not stepping down immediately and "impeding the party from supporting the M5S".
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Matteo Renzi pictured during his resignation speech. Photo: Alberto Pizzoli/AFP
Watching the third bloc
Italy's vote has drawn comparisons with the Brexit referendum in Britain and the election of US President Donald Trump because of the anti-immigration and anti-establishment rhetoric, raising concern in European capitals about instability.
Salvini overtook coalition partner Silvio Berlusconi's Forza Italia (Go Italy) party after promising to deport hundreds of thousands of "irregular" migrants, and railing against the European Union and its "failed currency".
On Tuesday Salvini said that the right "was the number one coalition and the hope for Italians" and he was open to negotiate with anyone who "shares our programme".
At the same time, he ruled out any "old-style political or cross-party agreement" and refused any alliance with the M5S.
For some political observers, it appears the Democratic Party could end up the kingmaker.
"The key question for the coming days is what the PD will do," said Giovanni Orsina, political science professor at Rome's Luiss University.
"Neither the right-wing alliance nor M5S are able to form a government alone. The question is therefore what the third bloc will do."
'Nothing will be as before'
M5S leader Luigi Di Maio also wants the prime ministerial nomination after his party hoovered up votes from Italians fed up with a slow economic recovery.
Di Maio, who is due to visit his hometown of Pomigliano d'Arco, an industrial base near Naples, later on Tuesday, will now face a difficult balancing act.
Any perception of cosy deals with other parties following the election risks alienating his core support from Italians angered by traditional politics.
A deal with the Five Star Movement could also divide the PD, where many are smarting from the movement's victories in traditional leftist heartlands.
"The world of Italian politics as we have known it for the last 25 years is over," wrote Corriere della Sera's editor Luciano Fontana.
"Nothing will be as before. The players, and the political landscape of the country have changed," he said.
By Dario Thuburn