The leader of Italy's anti-establishment Five Star Movement on Thursday said he was ready to negotiate for a "solid majority" in parliament, two days after the break up of the country's dysfunctional coalition government.

President Sergio Mattarella has held two days of crisis talks to see if a viable coalition can be formed following the break up of an alliance between Five Star (M5S) and the far-right League.

"In the last few hours we have started necessary discussions to find a solid majority," Five Star's Luigi Di Maio said after holding talks with Mattarella, without specifying with which party.

Prime Minister Giuseppe Conte resigned on Tuesday after months of alliance sniping and a bid by League leader and Interior Minister Matteo Salvini to force a snap poll, just 14 months after coming to power.

"The most convenient thing to do would be to go to the vote," Di Maio said.

"But the citizens voted for us to change Italy, and not the M5S."

He listed ten key policies, including a plan to slash the number of lawmakers in parliament from 950 to 605.

A proposed alliance between M5S and the opposition centre-left Democratic Party (PD) - previously almost unthinkable - has appeared to be gaining momentum.

After consulting with Matterella, PD leader Nicola Zingaretti said he wanted to form a new government but not "at any cost".

The PD and M5S have been at each other's throats for years - but an alliance would see Salvini kicked out of government, a powerful motive for compromise.

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.

Zingaretti on Thursday also highlighted past disputes with Five Star, saying "it is not an easy choice".

'Makeshift majority'

Mattarella, the 78-year-old head of state, wields important powers including the ability to pick prime ministers.

He has been exploring ways to form a new coalition but could also call an early election - more than three years ahead of schedule.

The president wants a concrete plan in place by Monday, a source close to him was reported as saying by the Repubblica daily.

After meeting with Mattarella on Thursday, Salvini appeared to backtrack on his earlier attempt to force new elections and offered to continue the coalition with M5S, as long as it could achieve things.

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 opinion polls suggesting the party would win a new vote.

Meanwhile, former premier Silvio Berlusconi, head of centre-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.

Indebted economy

The end of the unstable coalition government in the eurozone's third-largest economy has so far been welcomed by the markets, with the stock market up and Italian bonds rallying for a third day.

If a new coalition emerges, it will need to draft a budget this autumn that adheres to EU rules and energises the economy, which is on the brink of recession.

Some investors fear a snap election could lead to a League-led government with Salvini as prime minister, which could trigger a collision with Brussels over spending commitments in the debt-laden nation.

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.