Italian President Sergio Mattarella has set a Tuesday deadline for squabbling political parties to form a workable coalition government on Thursday, just two days after a dysfunctional populist alliance broke up throwing the eurozone's third-largest economy into political turmoil.

Mattarella, 78, concluded two days of crisis talks with key political players on Thursday to see if a viable coalition could be formed following the disintegration of the partnership between the anti-establishment Five Star Movement (M5S) and the far-right League.

"On Tuesday, I will hold further consultations and make the necessary decisions," Mattarella told reporters at the presidential palace.

"The crisis must be resolved in a timely manner and with clear decisions," he said.

After an intense 48 hours of political wrangling, Mattarella said a future coalition would need a specific program that could be passed in parliament.

If a coalition is not formed then Mattarella could consider a technical government or call an early election – just 14 months after the last parliamentary vote. The crisis comes after Prime Minister Giuseppe Conte resigned on Tuesday following months of alliance infighting and a bid by League leader and Interior Minister Matteo Salvini to force a snap poll.

A proposed alliance between M5S and the opposition center-left Democratic Party (PD) – previously almost unthinkable after years of vicious arguments –has been gaining momentum, with official talks set to begin.

After discussions with Mattarella, M5S leader Luigi Di Maio said he was ready to negotiate for a "solid majority" in parliament.

He listed 10 key policies, including a plan to slash the number of lawmakers in parliament from 950 to 605. His party later held talks and gave official clearance for formal discussions.

The PD also made positive noises with leader Nicola Zingaretti saying he wanted to form a new government but emphasized not "at any cost."

Although the PD and M5S have been at each other's throats for years, the traditional foes have a motive for compromise – power and kicking Salvini out of government.

Zingaretti has said the party would back an M5S coalition dependent on five conditions, including a radical shift in Italy's zero-tolerance policy on migrants crossing the Mediterranean.

Salvini – under fire from other parties for instigating the crisis – appeared to backtrack on his earlier attempt to force new elections.

After speaking to Mattarella, he offered to continue the coalition with M5S on condition it could pass legislation.

But at the same time he called for a snap election, saying "sovereignty belongs to the people."

Salvini has sought to exploit the League's growing popularity, with some opinion polls suggesting the party would win a new vote.

Meanwhile, former premier Silvio Berlusconi, head of center-right Forza Italia, warned against forming a government with "a makeshift majority."

It would make "a mockery of the voters and be a betrayal of their will," he said.

After last year's election it took months of wrangling before a government was formed.

If a PD-M5S tie-up emerges, it would realistically need support from smaller parties to be an effective government.

The parties are also considering a female prime minister, according to media reports, which would be a first for Italy.