ROME—Italians elected a right-wing coalition to lead the country, according to projected results, choosing an untested leader who will confront Europe’s gathering economic downturn and energy crisis resulting from Russia’s invasion of Ukraine.

Giorgia Meloni is favored to become Italy’s new prime minister after her Brothers of Italy party won the biggest share of the vote in Sunday’s parliamentary elections, according to projections based on counting nearly half of the votes for Italy’s Senate. She would require approval from junior partners in her coalition to assume the role.

Ms. Meloni’s party won just over 25% of the vote for the Senate, while her wider right-wing coalition won just over 43%, according to the projection. Their largest opponent, the center-left Democratic Party, won 19%. First projections for the lower house of Parliament showed similar percentages.

Ballots were counted at a Rome polling station on Sunday.

Photo: giuseppe lami/Shutterstock

“The situation in which Italy and the European Union find themselves is a particularly complex one,” Ms. Meloni told supporters in a brief victory speech early Monday, in which she called for “serenity and mutual respect” between Italy’s rival political parties after a fractious campaign.

Noting the record-low turnout of just 64%, Ms. Meloni said many Italians felt alienated from the country’s political institutions and vowed to work to rebuild people’s trust in their democracy. “The goal we set for ourselves as a political force is to make Italians proud of being Italian again, proud of waving the tricolor flag,” she said.

Italy’s electoral system, which strongly favors parties that run as part of a coalition, is expected to help the right to an ample majority in both houses of Parliament. The Italian election is the first big test of the European Union’s political cohesion as it confronts Russia’s attempt to redraw the continent’s post-Cold War order. Russian President Vladimir Putin’s restriction of natural-gas deliveries has sparked an energy-price crunch that, combined with other inflationary pressures, is expected to push much of Europe into a recession this winter.

Italian voters have, however, shifted toward parties with clear pro-Western stances, according to exit polls, while parties soft on Russia have performed poorly compared with the previous national elections in 2018, despite their efforts to court popularity by questioning Western sanctions on Moscow and resisting military aid for Ukraine.

The likely right-wing government will face difficult decisions over how to protect Italian households and businesses from sky-high prices for electricity and natural gas. Italy’s parlous public finances allow limited scope for fiscal largess. EU governments have so far struggled to agree on a collective intervention to tackle energy costs.

Italy’s high government debt of roughly 150% of gross domestic product, combined with its weak long-term growth record, makes it vulnerable to bond-market selloffs if investors lose confidence in the soundness of Rome’s fiscal policies, and dependent on the European Central Bank to keep its bond yields stable. ECB support has typically been conditional on Rome following cautious budget policies and enacting economic overhauls aimed at improving growth.

Aware that any adverse reaction by bond investors could further hurt Italy’s economic outlook, Ms. Meloni has sought to reassure financial markets that a government led by Brothers of Italy would seek to maintain fiscal discipline. That constraint could leave limited scope for the radical tax cuts that some in the right-wing coalition want.

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Like elsewhere in Europe, energy bills and the cost of living will be the most urgent issues for Italy’s next government. Ms. Meloni has vowed to act quickly to help Italian households and businesses, but also to avoid a spending spree that further raises Italy’s significant national debt.

Brothers of Italy and its allies want the EU to impose a cap on the price of natural gas and to decouple gas and electricity prices, said Giovanbattista Fazzolari, a senator and close aide to Ms. Meloni.

Increasing public spending to address the energy crisis “should be the measure of last resort,” Mr. Fazzolari said. “We want to intervene on pricing. If the European Union continues, irresponsibly, to fail to act, the Italian government should proceed on its own.”

Some EU officials have viewed Ms. Meloni’s rise with trepidation, fearing that Italy could become a less cooperative member of the bloc at the same time it faces severe economic and security crises. But many observers in Rome say Brothers of Italy is aware of how limited Italy’s room to maneuver is, given its economic fragility and need for good relations with other major actors in Europe and the West.

“Meloni knows she needs international backing to lead the country,” said Lorenzo Pregliasco, a political scientist and founder of opinion-polling company Quorum/YouTrend.

Voters lined up to cast ballots in Sicily on Sunday. Italian households and businesses are contending with high electricity and natural-gas prices.

Photo: orietta scardino/Shutterstock

For Italy, the EU’s third-biggest economy, Sunday’s results, if confirmed, mean that the right would take power for the first time since 2011, after more than a decade of eclectic, often short-lived coalition governments.

The outcome, if confirmed, is a personal triumph for 45-year-old Ms. Meloni, who has sought to end Italy’s recent history of technocratic governments. Ms. Meloni was the only major party leader to stay out of the bipartisan coalition supporting Italy’s departing prime minister, Mario Draghi. Her support has benefited greatly from being Italy’s only opposition. Her challenges will include sustaining that support in power, in a country where voters can become disenchanted with incumbents quickly.

Ms. Meloni has distanced herself and her party from their far-right background and run as a conservative whom Italy’s establishment and foreign allies, and financial markets, need not fear as a radical or disruptive force.

Her election campaign has combined broadly mainstream economic and foreign policies—including continued Italian support for Ukraine’s war effort against Russia’s invasion—with right-wing identity politics on immigration and gender. Brothers of Italy’s members and supporters range from centrists and moderate conservatives to some who have openly neo-fascist sympathies.

Emanuele Palermo, a 37-year-old car salesman from Rome, said he voted for Brothers of Italy for the first time on Sunday. “It’s an opportunity to restore Italy’s place on the world stage,” said Mr. Palermo, who voted for left-leaning parties in the past. “We shouldn’t behave like subjects of the European Union,” he said. Other issues that pushed Mr. Palermo to switch to Brothers of Italy are its hard-line stance on immigration and Ms. Meloni’s leadership.

“I like her determination, she inspires trust,” he said. “It remains to be seen if the trust I’m putting in her will be rewarded.”

Mario Draghi is leaving his position as Italy’s prime minister.

Photo: riccardo antimiani/Shutterstock

Edoardo Baiocco cast his vote for the 5 Star Movement, citing its flagship policy: a basic income for the poor. He doesn’t love Ms. Meloni, but said fears about a likely government led by her are overblown.

“She’s not a fascist. There is this terrible habit of labeling as fascist people we don’t agree with. She’s a woman who has very clear ideas,” said Mr. Baiocco, a professional collector of goods such as books and stamps. “I don’t believe she will really give Europe a hard time.”

Ms. Meloni has little government experience, apart from three years as minister for youth in the last administration of billionaire former Premier Silvio Berlusconi. Mr. Berlusconi, now a much-diminished political force, is the junior partner in Ms. Meloni’s right-wing alliance. His party won about 8% of the vote in Sunday’s election, according to the projection for the Senate.

Ms. Meloni’s challenges could also include managing her other ally: anti-immigration firebrand Matteo Salvini of the League Party, which has suffered a sharp drop in support since winning roughly one-third of the vote in 2019 European elections. On Sunday, the League won less than 9% according to the projected Senate results. Mr. Salvini has called for radical tax cuts and subsidies for energy bills, while questioning sanctions on Russia. However, Mr. Salvini’s poor result could call into question his authority within the League.

Another loser in Sunday’s election was the antiestablishment 5 Star Movement, which won over 32% of the vote in Italy’s 2018 national elections, but fell to just over 16% on Sunday, according to the projected Senate results. The 5 Star Movement, led by former Prime Minister Giuseppe Conte, is however claiming vindication after performing better than opinion polls indicated a few months ago.

Write to Margherita Stancati at margherita.stancati@wsj.com and Marcus Walker at marcus.walker@wsj.com