Italy’s prime minister, Giuseppe Conte, and his left-leaning coalition have won a vote of confidence in the Senate – the final step needed for the new government to exercise its full powers.

The move paves the way for the coalition between the anti-establishment Five Star Movement (M5S) and the centre-left Democratic party (PD) to potentially reverse the hardline immigration policies of the former interior minister Matteo Salvini.

Senators voted 169-133 in favour of the new EU-friendly government, aimed at drawing a line under a crisis sparked by Salvini, the far-right leader of the League.

Conte, who is on his second mandate as prime minister, is attempting to turn the page after the collapse of M5S’s ill-fated 14-month alliance with the League.

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The vote followed a heated debate during which senators from opposition parties shouting insults against Conte.

“I know someone who seemed like a premier for months,” said Salvini, who was deputy premier under Conte for 14 months. “I don’t know what happened then, what they promised him. I expect a premier to have an idea for Italy, not continual insults. He is a man who is aligned with power, without dignity.”

Conte said: “I see no dignity in your volte-face. Assigning one’s faults to others is the most linear way to dodge responsibility for life, a sure way, but not the best, to save one’s leadership. To err is human, but to give other people the blame is the best way to keep the leadership of your party.”

Italy was plunged into chaos last month when Salvini withdrew the League from its fractious alliance with M5S as he sought to exploit his party’s popularity to bring about snap elections and become prime minister.

The move threatened to create a fully far-right government. But Salvini, whose tactics have dented his popularity in recent weeks, had not banked on M5S teaming up with the PD. The two parties are longstanding enemies and the two largest parties in parliament.

After two weeks of negotiations, last week Conte announced his team of ministers, pledging that the new coalition would be less antagonistic and more respectful than the previous one. The list included Roberto Gualtieri, an influential PD member of the European parliament, as economy minister. The M5S leader, Luigi Di Maio, will be foreign minister.

Luciana Lamorgese, a veteran of the interior ministry in charge of planning refugee and migrant reception centres in northern Italy, has succeeded Salvini in his former role.

Many challenges lie ahead. Last week the parties published a 26-point programme intended to underpin the government. At the top of the list was a commitment to use the forthcoming budget to help to stimulate economic growth, but also a promise that it would not endanger public finances.

Italy has the second-largest debt burden in the EU as a proportion of economic output, and the pact called for greater flexibility from Brussels to overcome the “excessive rigidity” of existing budget rules.

Many analysts have cast doubt on how long the new coalition will last. Others argue that the prospect of Salvini forming a far-right government with Brothers of Italy, a party with a neo-fascist lineage, after a new election will hold the coalition together. According to polls, the League is still the biggest party in Italy despite losing some of its popularity in recent weeks.

“Today the division between the closed palace and the Italy in the street is evident,” Salvini said on Monday. He has called for a demonstration to be held in Rome in October.