When Prime Minister Giorgia Meloni of Italy convenes the leaders of the Group of 7 countries on Thursday at a luxury resort hotel overlooking the Adriatic Sea, she might be forgiven for thinking her guests are seeking a refuge.

Except for Ms. Meloni herself, every one of the leaders is arriving at the meeting beleaguered, embattled or endangered — an ill-starred convergence that speaks to the political tremors rattling across the West. It also doesn’t bode well for the results of a gathering that already faced vexing challenges, ranging from Russia’s war in Ukraine to China’s global economic competition.

Britain’s prime minister, Rishi Sunak, is three weeks away from an election in which his Conservative Party is expected to be swept out of power. President Emmanuel Macron of France has called a snap parliamentary election after his party suffered heavy losses to the far right in European elections.

Chancellor Olaf Scholz of Germany and his Social Democratic Party were humbled in those elections as well, while President Biden is in a dogfight with his predecessor, former President Donald J. Trump. Even Prime Minister Fumio Kishida of Japan faces rising unrest within his Liberal Democratic Party and may lose his job this autumn.

Prime Minister Justin Trudeau of Canada, who faces his own disenchanted public after more than eight years in office, spoke for his fellow leaders when he lamented the surge of populism in Europe and the United States.

“We have seen around the world a rise of populist right-wing forces in just about every democracy,” Mr. Trudeau said on Monday. “It is of concern to see political parties choosing to instrumentalize anger, fear, division, anxiety.”

Anxiety about the role of the Group of 7 is nothing new: These seven countries account for a diminishing share of global gross domestic product. The leaders of China and Russia are conspicuously absent. (Russia was suspended from the group in 2014 after it annexed Crimea and left permanently in 2017.)

In a gesture to the changing world, Ms. Meloni has invited an A-list of non-Western leaders to Italy: Prime Minister Narendra Modi of India, President Luiz Inácio Lula da Silva of Brazil, President Recep Tayyip Erdogan of Turkey, and the president of the United Arab Emirates, Prince Mohammed bin Zayed. She also invited President Volodymyr Zelensky of Ukraine and Pope Francis.

Some of these leaders shoulder their own burdens. Mr. Modi was just elected to a third term, but his party’s parliamentary majority vanished. Mr. Erdogan suffered setbacks in local elections. While these leaders will not take part in the core sessions, some will hold separate meetings with Mr. Biden and other leaders, serving as a reminder of how power dynamics in the world are shifting.

Domestic politics will intrude on the G7’s business in ways large and small, according to analysts and diplomats. With Britain on the cusp of a vote that is likely to bring in a new government, Mr. Sunak is not expected to sign up to major commitments on trade with China or sanctions against Russia. Instead, his participation in the summit could end up being a farewell tour.

“How can you commit to anything if you’re going to have a change in government?” said Agathe Demarais, a senior policy fellow and director of the geoeconomics initiative at the European Council on Foreign Relations in London. “‘Wait and see’ is probably going to be the keyword.”

While Mr. Biden does not have to face voters until November, analysts said he, too, may be preoccupied by his election struggles back home, as well as by personal issues, including the conviction of his son, Hunter, on three felony counts of lying on a federal firearms application in 2018.

To a lesser degree, domestic politics may also constrain Mr. Scholz and Mr. Macron. Both are in more vulnerable positions after the advances made by far-right parties in European Parliament elections.

A surge in populism could divide the Western leaders on some issues and play to advantage of their biggest rivals on others. Far-right parties tend to be more hostile to free trade but friendlier to China and less supportive of harsher sanctions on President Vladimir V. Putin of Russia. These are all issues that will loom large when the leaders sit down on Thursday in the coastal town of Fasano.

The Biden administration has pushed Europe to impose higher tariffs on China’s exports of electric vehicles, batteries and semiconductors, as it did in May. It is trying to drum up support for secondary sanctions on Russia, a major escalation of pressure that would go after companies that do business there.

But Ms. Demarais said, “The Europeans know that Trump could undo anything that Biden promises.” And given their own weakened position, she said, “If they sign an agreement, there’s also a risk that they wouldn’t get parliamentary approval for it.”

Mr. Macron, having lost in the European vote to the far-right party of Marine Le Pen, dissolved the French National Assembly and called snap elections that will end on July 7. Though he will be president for another three years, regardless of the outcome, he is weakened and could be forced to share power with an opposition prime minister.

Political analysts have likened Mr. Macron’s roll of the dice to the fateful decision by David Cameron, the former British prime minister who is now the foreign secretary, to call a referendum on Brexit in 2016.

In Germany, Mr. Scholz’s Social Democrats finished third in the European elections, after the opposition Christian Democrats and the far-right Alternative for Germany, which swept the former East Germany. Mr. Scholz’s coalition partners, the Greens and the Free Democrats, also fared badly.

While Mr. Scholz is unlikely to call a new election like Mr. Macron, he is under pressure to do so. He and his government are deeply unpopular, their internal bickering a recipe for paralysis. German support is viewed as critical for tariffs against China, a major competitor in electric vehicles, as well as secondary sanctions against Russia.

Even before the political upheaval, Europe and the United States could not agree on what to do with the nearly $300 billion in Russian foreign exchange reserves that are frozen by Western banks. The White House initially wanted to confiscate the entire sum to use in rebuilding Ukraine. But European countries balked, fearing that such a move would destabilize the global financial system.

Now, the G7 countries are weighing a plan to amortize the frozen assets to get Ukraine a quick $50 billion or so, and then use the profit and interest earned to pay back the debt over time. That would supersede an E.U. plan to just use the profits and interest for Ukraine. But there remain disagreements over how such a debt would be guaranteed if the assets are returned or interest rates collapse.

Diplomats praised Ms. Meloni’s attempt to reach out to new leaders, though Peter Ricketts, a former national security adviser of Britain, said, “It betrays a justified feeling that the G7 is an old grouping now.”

The clearest winner in all this may be Ms. Meloni herself. Though she, too, came to power at the helm of a far-right party, she has cultivated an image as someone with whom Europe’s centrist leaders can work. For three days, she will hold court at Borgo Egnazia, a resort favored by celebrities like the pop star Justin Timberlake, who married the actress Jessica Biel there in 2012.

For all the bickering over China trade or Russian sanctions, diplomats said the leaders were unified on the two great issues of the day: support for Ukraine, and for President Biden’s attempts to broker a cease-fire in the Israel-Gaza war.

“From the point of view of the leaders,” Mr. Ricketts said, “this is probably a welcome diversion from a difficult domestic environment.”