Italy's president has asked Premier Matteo Renzi to delay stepping down until parliament can pass a critical budget law due later this month.

The presidential palace said Italy's head of state, President Sergio Mattarella, met Mr Renzi on Monday evening at the presidential palace in Rome.

The palace said Mr Renzi told the president "it's not possible to continue in his post" as premier following the resounding defeat on Sunday of a referendum on constitutional reforms that Mr Renzi promoted.

Mr Mattarella, considering how parliament needs to complete its approval of the budget law, "asked the premier to delay his resignation until that task is accomplished".

The news came as calls were mounting from populist and other opposition leaders for quick elections in the country.

"With the referendum vote, the Italians have expressed a clear political signal - the desire to go as soon as possible to elections," wrote Vito Crimi and Danilo Toninelli, two of the top leaders of the populist 5-Star Movement in a piece accompanying the blog of Movement founder, comic Beppe Grillo.

Mr Mattarella can ask someone else to try to form a government and work with the same Parliament, at least for a few months.

Mr Renzi's squabbling Democrats are the biggest party in the legislature, which could lead the president to tap someone from the Democratic Party fold.

But Mr Renzi, as head of the party, could very well decide that early elections are the best course, to avoid the risk of angering the electorate by delaying, said Mario Calabresi, editor and commentator at La Repubblica.

Demands mounted from opposition parties, eager to capitalise on Mr Renzi's political misfortunes, for elections to be called far ahead of the spring 2018 due date.

Former three-time premier Silvio Berlusconi, the centre-right leader, was among them.

"We are certain that the president of the republic will know how to pinpoint the most correct solution to assure Italians... the possibility to vote and finally choose, after three non-elected governments," he said.

Mr Berlusconi himself was forced to resign in 2011 amid growing international concern over Italy's sovereign debt crisis and was replaced by economist Mario Monti, without elections.

After Mr Monti's government unravelled, a Democrat, Enrico Letta, was appointed.

Mr Renzi, as the Democratic Party leader, used party manoeuvring to push Mr Letta out of office and take the premiership for himself in February 2014.

Angling to gain national power for the first time are the 5-Stars, who did well in mayoral races earlier this year, including winning City Hall in Rome, Italy's capital.

Mr Grillo himself cannot hold office because of a manslaughter conviction arising from a car accident.

Also energised by Mr Renzi's debacle is the anti-immigrant Northern League, whose leader has allied himself with far-right figures in Europe including France's Marine Le Pen, head of the National Front.

Northern League leader Matteo Salvini called for an immediate election this winter "because real change happens only through electoral victory".

While Italy's opposition parties were united in antipathy for Mr Renzi's policies and reform course, they have little else in common and have already begun vying to position themselves for eventual campaigning for Parliament.

Since the Italian president tries to ensure Parliament can carry out its full five-year term, analysts expect that Mr Mattarella will appoint a transition government to draft a new election law that could satisfy parties worried that, the way the rules now stand, their forces might be at a disadvantage.

Among the names touted to head it are Mr Renzi's finance minister, Pier Carlo Padoan; the president of the Senate, former anti-Mafia prosecutor Pietro Grasso; and Foreign Minister Paolo Gentiloni.

European partners sought to downplay the risk for the common euro currency and European unity.

"This is a crisis of government, not a crisis of state, and it's not the end of the West. But it's certainly not a positive contribution against the backdrop of the crisis in Europe," German foreign minister Frank-Walter Steinmeier said in Athens.

Investors had been anticipating Mr Renzi's defeat for several days, and had sold off Italian stocks and bonds.

Monday's sanguine market reaction can also be attributed to the fact that Italy's markets indirectly enjoy a big backstop from the European Central Bank.