Salvini and 5Star leader Luigi Di Maio were expected to unveil the main points of their government deal Monday and inform Mattarella of their candidate for prime minister, following frantic negotiations over the weekend.
Italy's anti-establishment 5-Star Movement and the far-right League remain locked in talks to forge a common policy program and said they would not be able to present it to the head of state on Sunday as planned.
Both leaders insisted Monday that no names within their future cabinet would be made public before they had been approved by Mattarella. "I'm proud that we are discussing, even heatedly, about the kind of Italy we want to create", said Salvini, adding there were differences on issues including immigration, justice reform and infrastructure.
Luigi Di Maio, leader of the Five Star Movement, speaks at a news conference following a meeting with Italy's President Sergio Mattarella at the Quirinale Palace in Rome, Italy.
At the March polls, Five Star emerged as Italy's largest single party in parliament by far after winning almost 33% of the vote.
After meeting Mattarella for a quick round of consultations on Monday, the League's leader Matteo Salvini said there were still "key issues" to be settled with the 5Stars.More news: Union Cabinet reshuffle: Goyal gets finance portfolio; Smriti out of I&B Ministry
Mr Di Maio said he and Mr Salvini agreed "that we won't publicly name names" of their choices for premier.
Italy has been in political deadlock since an inconclusive March 4 election, which was dominated by concerns over a struggling economy, the refugee crisis and illegal immigration.
Salvini's League won 17 percent of votes in March, but it was part of a right-wing alliance including Berlusconi's Forza Italia that garnered 37 percent of the vote.
In what looked like mutual posturing, Di Maio said any deal with the League needed to win the support of M5S members through an online vote, while Salvini claimed he was making a sacrifice in keeping alive coalition talks.
In a no-deal scenario, Mattarella has said he would appoint a "neutral government" to take care of urgent business - namely an European Union summit in late June on migration, budget and banking reforms - and to organize new elections in July or September-October.
Their flagship economic measures are also seen as too ambitious and expensive for a heavily indebted country like Italy, which has the second-largest debt in the eurozone after Greece.