The fate of Italy’s coalition government lies with the far-right deputy prime minister, Matteo Salvini, a day after the prime minister threatened to resign if Salvini’s League and its coalition partner, the Five Star Movement (M5S), could not patch things up.

Giuseppe Conte, a law professor who was plucked from obscurity a year ago to steer the coalition, issued the ultimatum to Salvini and M5S’s Luigi Di Maio during a press conference on Monday night, urging them to set aside their many differences and “revive the spirit” of the coalition government’s early days, or seek new elections.

The bickering has intensified since the League eclipsed M5S in the European elections last month, and has stalled progress on policies. Financial markets are jittery as economic growth hovers at about zero.

Conte said: “I personally remain willing to work with the utmost determination, but I can’t make this choice alone. If they cannot assume responsibility then I will simply resign my mandate.”

He said he was unsure how long the government would last, while insisting that for as long as it stayed together, EU financial rules must be respected. Italy could soon face an EU infringement procedure for failing to reduce its debt.

Salvini and Di Maio, who are reported to have had a cordial conversation by phone, initially declared their loyalty to Conte, saying the government would move forward. But by Tuesday morning, they were at odds again, with Di Maio accusing Salvini of plotting to derail the coalition.

Francesco Galietti, the founder of Policy Sonar, a Rome-based consultancy, said: “If Conte thought he could move things with yesterday’s intervention then he miscalculated the situation massively. It was quite frustrating as you could tell that he’s not in control of the ship.”

Salvini issued an ultimatum on Tuesday. “If in 15 days we are still having the same discussions with the same delays and postponements then there will be a problem,” he said.

Over the past year, the two parties have rowed over everything from immigration to ministerial ethics. Their main achievement has been the rollout of M5S’s flagship basic income for poorer people.

Further clashes loom over granting fiscal autonomy to wealthy northern regions, a key policy of the League, and easing bureaucracy in public tenders for infrastructure projects.

Salvini has repeatedly pledged to challenge EU deficit rules in order to include a flat tax in Italy’s 2020 budget. The budget is negotiated during the autumn period, so if the government falls and no alternative parliamentary majority is found, elections would need to take place by September.

Franco Pavoncello, a political science professor and the president of John Cabot University in Rome, said: “I have a feeling they have reached their limit, but the ball is very much in Salvini’s court.

“He has to decide whether to bring down the government now and then have the problem of unbearable interest rates the next day, which I’m not sure he can face, or stick with it and come up with €40bn for a fiscal manoeuvre [for the 2020 budget]. It’s a very problematic situation in terms of government accounts.”

The odds of a government collapse are greater now than they were last week, when Salvini claimed the League’s EU elections success would not prompt a crisis. M5S’s unity has been weakened by the fragility and erosion of the party’s supporter base over the past year. Di Maio called a confidence vote on his leadership last week.

Galietti said: “It could branch out in two directions: either M5S accepts becoming the political manservant of Salvini, or we have a divorce. Either way, Salvini has no reverse gear. The very idea that he can pause and restore some kind of idyllic situation is childish. You can feel the jungle beat getting louder and louder.”