Half a decade ago, upon her party securing a 6 percent share of the votes in the European Parliament elections, Giorgia Meloni attempted to uncork a bottle of bubbly, only to have the cork comically dart among her supporters.

Fast forward to this week, Ms. Meloni, now serving as Italy’s prime minister, emerged triumphant in the elections, with her Brothers of Italy party garnering nearly 29 percent of the votes. In celebration, she and scores of her party members gathered at a luxurious hotel in Rome, where waiters paraded wine bottles in silver containers brimming with ice. This victory held particular significance as Ms. Meloni stood alone among leaders of major Western European nations that emerged stronger from the elections.

The timing of this elevation could not have been more opportune for Ms. Meloni, as Italy gears up to host a three-day summit of the Group of 7 major economies starting on Thursday. This event presents another chance for her to project herself as a respected member of the league of the world’s most influential figures.

“With the mightiest government of all the nations, we march to the G7 and Europe,” she declared to her supporters in the early hours of Monday once the results were clear. “Our forward march was unstoppable.”

Her ascent to the prime ministership in 2022 rattled the European establishment owing to her far-right stances, skepticism toward the EU, and association with post-fascism. However, she has now earned recognition from the establishment as a pragmatic partner on vital global issues.

Ms. Meloni’s approach is being observed as a blueprint by other far-right leaders seeking acceptance into mainstream politics.

A similar shift has been noted in France, where Marine Le Pen has softened her stance on critical matters and refined her public image. Her National Rally party’s strong showing in the European elections, securing over 30 percent of the vote, prompted President Emmanuel Macron to dissolve the National Assembly and call for fresh parliamentary elections.

“Meloni’s administration has had a positive ripple effect across Europe,” remarked Giovanni Donzelli, a Brothers of Italy legislator on Sunday evening. “All of Europe witnessed a paradigm shift—recognizing that the right wing can govern effectively.”

In recent times, Ms. Meloni has garnered attention from both the European center-right seeking an alliance and from farther right-wing parties rallying to construct a united nationalist front.

While the center maintained its position in the new European Parliament, Ms. Meloni could emerge as a pivotal figure in individual votes, including the imminent re-election of Ursula von der Leyen, the European Commission president, who requires the legislature’s approval for a second term.

Experts suggest that Ms. Meloni may opt to back Ms. von der Leyen to enhance her influence in Brussels.

“Meloni is poised to become a significant force in Europe,” declared Mujtaba Rahman, the managing director for Europe at the Eurasia Group consultancy. “As she leans toward the center and adopts a constructive approach, she is bound to reap ample rewards.”

On a broader global scale, Ms. Meloni has solidified her role as a key player in matters like backing Ukraine, setting her apart from other hard-right factions that tend to lean pro-Russian.

This stance has earned her favor with the cohort of Western leaders convening this week in the southern Italian region of Apulia, especially following the recent elections.

“All eyes are on her,” observed Roberto D’Alimonte, a political scientist at the LUISS Guido Carli University in Rome. “Her stature has risen significantly.”

Among the anticipated G7 attendees are President Biden, Prime Minister Justin Trudeau of Canada, Rishi Sunak from Britain, President Emmanuel Macron of France, Chancellor Olaf Scholz of Germany, and Prime Minister Fumio Kishida of Japan. Also expected to be present are Ms. von der Leyen and Charles Michel, the president of the European Council.

Ms. Meloni has extended invitations to Pope Francis, President Volodymyr Zelensky of Ukraine, India’s recently re-elected Prime Minister Narendra Modi, and Brazil’s President Luiz Inácio Lula da Silva, along with several African leaders. She intends to focus part of the summit on her proposed plan for development and collaboration with Africa.

The gathering is set in Borgo Egnazia, a lavish resort featuring shimmering pools encircled by rosemary shrubs and olive trees. The stone-built townhouses and villas are laden with baskets of almonds and lemons, while the narrow pathways are flanked by rusty bicycles and wooden carriages accumulating signs of age.

However, the entire venue was constructed in the early 2000s on land cleared by Mussolini to erect an airbase. The resort replicates an ancient Apulian town and farmhouse in a project that some locals liken to a Mediterranean Potemkin village.

Past visitors to the luxurious resort, aside from world leaders, include Madonna, the Beckhams, and the wedding couple Justin Timberlake and Jessica Biel.

“Meloni is determined to create a lasting impression, and I am confident she will achieve that,” remarked Romeo Di Bari, 41, a shopkeeper in the town of Alberobello, scheduled for a visit by the leaders’ partners. In a recent afternoon, boyfriends kneeled on the cobblestones to capture their girlfriends twirling around the iconic pointy trulli huts.

In the nearby city of Bari, locals praised Ms. Meloni for restoring prestige to their region and country.

“Our nation stands at the forefront,” stated Giovanni Pirlo, 68, a retired surveyor. “Our nation was perennially marginalized; with Meloni at the helm, change is underway.”

Ms. Meloni has deftly balanced her personas as a grassroots figure and an international diplomat. She has insisted on a familiar relationship with Italians, encouraging them to pen “Giorgia” on their ballots, emphasizing that she defended Italy’s interests in Brussels by aiding the passage of conservative policies on immigration and the environment.

At home, Ms. Meloni leads a stable coalition bolstered by two smaller parties reliant on her leadership. Forza Italia, following the demise of its founder Silvio Berlusconi last year, secured approximately 10 percent of the European Parliament vote after running a campaign that nostalgically featured Mr. Berlusconi’s name and visage on billboards. Matteo Salvini’s League party, targeting Ms. Meloni’s right-wing electorate, saw its vote share plummet to 9 percent this year from 34 percent in 2019.

Italy’s nationalist leader’s most pressing challenge could be the nation itself, experts suggest.

Italian productivity lags behind the EU average, and wages remain stagnant for the most part. While employment figures have risen, youth unemployment continues to plague the South, with tens of thousands of young Italians departing the nation annually.

In Savelletri, near the G7 venue, locals frequent a cafe adjacent to two newly erected helipads, while military vehicles patrol the vicinity.

Stefano Martellotta, a 51-year-old fisherman, expressed minimal interest in what he referred to as the G7 “spectacle.” His foremost concern was his two sons, aged 22 and 27, who relocated to the Netherlands to work in restaurant kitchens because in Italy, “they aren’t offered a decent wage,” he remarked.

“It’s dire for us, witnessing our youth drift away,” lamented Annamaria Santorsola, 75, a mother and grandmother, highlighting the necessity for “employment, not the G7” in their region.