Two days after Italy's populist government collapsed, the centre-left Democratic Party (PD) leader has told the president he will try to reach a deal with the populist Five Star party.
Nicola Zingaretti said Italy needed a "turning-point government" but made a series of demands.
President Sergio Mattarella wants a swift government deal, otherwise Italy faces new elections.
He said on Thursday evening that the parties had asked for more time.
"On Tuesday, I will hold further consultations and make the necessary decisions," the president told a news conference.
Five Star has set its own 10 conditions.
After meeting the president earlier on Thursday, leader Luigi Di Maio said he was ready to negotiate for a "solid majority" in parliament but made no mention of the centre left.
He warned of a repeat of Italy's 2011 crisis, which led to a technocrat government taking power and then went on to announce a list of priorities.
Prime Minister Giuseppe Conte resigned in dramatic fashion in parliament on Tuesday, after one of the two populist leaders in the coalition, Matteo Salvini, pulled the plug on the government, demanding a vote of no confidence.
Mr Salvini, whose right-wing, nationalist League is leading the opinion polls, is seeking new elections, 14 months after he went into coalition with Five Star.
Will the centre left return to power?
The head of the centre-left PD was among the first of the party leaders to visit the president on Thursday morning. His potential coalition partner, Five Star, met Mr Mattarella late in the afternoon.
The two parties, which until now have never seen eye to eye, had already held exploratory talks in which both expressed initial interest in a deal.
Mr Zingaretti came up with several conditions for Five Star to meet, including loyal membership of the European Union, giving parliament a central role and a reversal of Mr Salvini's anti-immigration policies.
"We expressed our willingness to the president to verify the formation of a different majority," he said, emphasising he wanted a government that brought an end to the policies and politics of the previous coalition.
The PD wants a new prime minister to replace Mr Conte, currently acting as caretaker, and some reports suggest Italy could have its first woman leader.
The president also met Mr Salvini as well as the leaders of the centre-right Forza Italia party and the far-right Brothers of Italy.
Forza Italia leader Silvio Berlusconi warned that without a centre-right majority in the next government there would have to be new elections. Mr Salvini said he would be prepared for another alliance with Five Star, even though he preferred elections.
What have the populists said?
Coming out of his meeting with President Mattarella, Mr Di Maio said he was keen to forge a coalition deal but was not specific about a possible partner.
"We will not allow the ship to sink and let Italians pay for it," he said.
The main priority for Five Star is reducing the number of parliamentarians in the upper and lower houses from 950 to 605. Mr Di Maio also called for a "green new deal" involving a shift towards renewable energy, as well as reforms to the judiciary, the banking system and public broadcaster Rai.
What are the sticking points?
One of the potential obstacles for a coalition would then be who would become prime minister. Neither Mr Zingaretti nor the Five Star leader have shown any interest in the job and attention has turned to a possible outside candidate.
More significant differences may emerge over policies:
- On Five Star's key demand of a cut of 345 parliamentarians, the PD may only agree to this in conjunction with broader constitutional reform
- The two parties are also expected to have differences over Italy's 2020 budget, which will have to comply with EU deficit rules. Italy is the third biggest economy in the eurozone but, at 132%, it has the second biggest debt in proportion to its output.
- The centre left will seek the rollback of many of the League-sponsored immigration measures that brought about the closure of ports to migrants. Although they were pushed forward by Matteo Salvini, Five Star ultimately agreed to them.
If the two parties fail to reach agreement, autumn elections appear likely, with Mr Salvini's nationalists eyeing victory.