Matteo Renzi will remain in office for at least a week after Italy’s head of state asked the centre-left prime minister to “freeze” his resignation temporarily until the senate passed a 2017 budget.

Renzi met Sergio Mattarella on Monday at the presidential palace – the Quirinale – in order to formally submit his resignation following a stunning defeat in a referendum on Sunday. Renzi was expected to step down immediately but his departure could now be delayed until Christmas.

Mattarella signalled that he will not call snap elections in response to the referendum results, putting him on a collision course with populist and rightwing parties that want a new poll to be called right away.

The Sicilian head of state said he believed it was important for Italy’s institutions to respect “commitments and deadlines”, and that they worked hard to find solutions that were worthy of the “demands of the time”.

While the president must always appear to be independent of political allegiances, his comments were taken as a clear sign that he believed the current government needed to fulfil its obligation to not only pass a budget but also make changes to an election law that has been put in flux by the referendum results.

Renzi’s months-long campaign to convince Italians to vote yes and overhaul the constitution and parliament was roundly rejected by 59.1% of voters on Sunday, on a turnout of 68%. The high interest in the plebiscite did not escape Mattarella, who said it was a “testament to a solid democracy [and] an impassioned country capable of active participation”.

Mattarella’s call for “serenity” after Italy was plunged into political chaos by the vote may have assuaged worries in Europe about what Renzi’s defeat signified for Europe, Italy’s fragile banking system, and the future of the euro.

Germany’s foreign minister, Frank-Walter Steinmeier, said the result was a “concern”, while finance minister Wolfgang Schäuble said Italy ought to continue on an economic path that had been adopted by Renzi.

The results, however, were celebrated by French far-right candidate Marine Le Pen who said that, with the no win, Italians joined the British in turning their backs on “absurd European policies which are plunging the continent into poverty”.

The anti-establishment Five Star Movement (M5S) and the xenophobic Northern League both said they wanted snap elections.

Beppe Grillo, the former comedian who co-founded the movement, said the referendum results had “opened a window” to the party possibly assuming power. Luigi Di Maio, one of M5S’s rising stars, also declared that the populist movement was ready to form a government, while the Northern League head, Matteo Salvini, said his fringe party – which has its roots in secessionism – ought to be considered a “serious alternative”.

Salvini said the result – and the strong showing of the far-right candidate in the Austrian presidential election on Sunday – was a clash of “all against one”.

Martin Radjaby, managing director of the agency Jung von Matt, which coordinated the winning campaign, told the Guardian: “Van der Bellen’s success in Sunday’s election has shown that liberals can reclaim subjects currently occupied by populists and nationalists, such as tradition and patriotism.”

Most analysts dismissed the idea that the main forces behind the no vote in Italy would succeed in their bid for immediate elections. While the situation could change, most agreed that Mattarella would most likely be able to install a new prime minister and caretaker government, which would oversee changes to the electoral laws that would make it more difficult for the M5S or Northern League to win a strong majority in parliament.

If Mattarella is able to cobble together a coalition government, it could delay elections until as late as 2018, although some believe an election could still be called next year.

A caretaker government could be led by Pier Carlo Padoan, the finance minister, or Pietro Grasso, the speaker of the senate, among other members of the Democratic party.

Most observers believed that, with or without Renzi at the helm of the party, the ruling Democratic coalition would likely stay intact and pursue the legislative issues at hand, possibly with the help of Silvio Berlusconi, the former premier and head of the Forza Italia party.

After weeks of crisscrossing the Italian peninsula to try to persuade Italians to vote si (yes), the final results on Monday showed that only relatively small pockets of voters backed the prime minister’s proposals, including areas of his native Tuscany, Emilia-Romagna, and the city of Bolzano.

Italians living abroad also backed the plans, but the no victory was overwhelming, with areas of southern Italy, such as the Sicilian port city of Catania, voting more than 70% against change.

For some Sicilians, Grillo became a larger-than-life figure in 2012, when he dramatically swam the 3.5km stretch dividing the southern Italian island from its mainland as a way of marking his arrival in the region.

“I would like to see Grillo as Italy’s next prime minister,” said Giuseppe Tornabene, a 27-year-old waiter. “Renzi made lots of promises at the beginning, and made us feel loyal towards him, but in the end he didn’t fulfil anything. Grillo is more honest, his party seems to understand the people more and is closer to us.”

Rosario, a 29-year-old teacher, also described himself as a “sympathiser of the Five Star Movement” and said he would prefer either one of Movement’s young rising stars, di Maio or Giovanni di Battista, as leader. “I didn’t agree with any of the things Renzi did during his time in office,” he said.

“And the way he handled this campaign was all wrong – he made it about him and not about the constitutional reforms, which I agree needs to be changed.”