Italy’s full senate will meet on Tuesday to set a date for a no-confidence vote in the government after political leaders failed to unanimously agree on a schedule.

Matteo Salvini’s far-right League party issued a motion of no confidence in prime minister Giuseppe Conte’s government last week, after it dramatically withdrew support for its fractious coalition with the anti-establishment Five Star Movement (M5S) in a push for snap elections. The heads of political groups have clashed over when the vote should take place.

Salvini is eager to capitalise on his popularity and wants the vote this week. Silvio Berlusconi’s Forza Italia and the smaller far-right party, Brothers of Italy, have joined the League in aiming for 14 August, after a commemoration service marking the first anniversary of Morandi bridge collapse in Genoa, in which 43 people died.

M5S, the centre-left Democratic party (PD) and others opted for 20 August.

Salvini, who is deputy prime minister and interior minister, has also threatened to withdraw his seven ministers in order to topple an administration that he says is no longer viable.

If Conte loses the confidence vote, the government would have to be dissolved and elections held within 45 to 70 days.

Knowing the League could soon seize power, factions from within M5S and the rival PD had discussed teaming up to delay elections by carving out a caretaker government in order to pass the 2020 budget.

The PD faction was led by the former prime minister Matteo Renzi, who still wields influence within the party but is unpopular with voters. The M5S leader, Luigi Di Maio, said late on Monday that “nobody wants to sit at the table with Renzi”, while the party’s founder, Beppe Grillo, called him a vulture. The PD leader, Nicola Zingaretti, also ruled out such a move, saying it would be a “gift to the dangerous right”, while appealing for unity within his party.

Di Maio rallied his MPs on Monday morning and had reportedly accused Salvini of betraying the government contract for his own interests. Di Maio said on Friday that he favoured a return to the polls, but that first he first wanted parliament to adopt a reform to cut the number of senators and deputies from 951 to 605.

The decision to dissolve the government and call fresh elections rests with the president, Sergio Mattarella. He could install a technical government, but that option also tends to be unpopular with voters.

Salvini has been touring Italy’s beaches since last week, calling on supporters to give the League, which is nearing 39% in polls, “full power” to “save Italy”. He said he would meet his allies, the Brothers of Italy and Silvio Berlusconi’s Forza Italia, this week.

The three parties joined forces before national elections in March 2018 and compete together at the regional level. A coalition between the League and the Brothers of Italy, a party with a neo-fascist lineage, would create a fully far-right government in a major western European nation.

“We genuinely rule out that there is any life left in this parliament and we consider elections in October as a baseline scenario,” Policy Sonar, a Rome-based political consultancy, said in a note.

Franco Pavoncello, a political science professor and the president of John Cabot University in Rome, said: “There are people who don’t want elections right away, others who want them desperately and others who are sort of neutral. But I think it’s a long way to Tipperary for the elections … the last time Italy held a vote in the autumn was in 1919, just before Benito Mussolini’s victory.”