They come from far corners of the globe, speak different languages, span the ideological spectrum and range in age from 43 to 80. But one thing President Biden and the other leaders of the Group of 7 meeting in Japan this weekend have in common? They’re not all that popular at home.

For Mr. Biden and his counterparts from the world’s leading industrial powers, it is an age of democratic discontent when electorates seem perpetually dissatisfied with the presidents and prime ministers they have chosen. Each leader is in hot water for different reasons, but their shared struggles highlight the fragility of free societies in a time of deep political and cultural divisions.

That has made this year’s summit meeting in Hiroshima, Japan, something of a “lonely hearts club,” in the phrase of one specialist, where unloved leaders can commiserate over their domestic troubles and trade ideas for how to get back into the good graces of their voters. A few days away from home to engage peers on the world stage can be a welcome relief for battered leaders, a chance to strut and posture and play the role of statesman shaping the forces of history.

But their troubles have a way of following them and can limit their options and influence. Mr. Biden started his morning on the opening day of the three-day meeting on Friday not with an elevated discussion of affairs of state but with a half-hour phone call back to Washington to check on negotiations with Republicans over the more prosaic yet profoundly consequential issues of spending and debt. He ended the day by skipping out about 90 minutes early from the leaders’ gala dinner on Miyajima island to take another call from home on the spending talks.

“The upshot,” said Suzanne Maloney, director of the foreign policy program at the Brookings Institution, “is an environment in which the leaders of the world’s most powerful democracies have to engage with an ever more challenging world, even as they’re on shaky ground at home. This can fuel doubts among our allies and overconfidence among our adversaries, and leave us all more vulnerable as a result.”

Survey data compiled by Morning Consult in recent days indicated that the leaders of only four out of 22 major countries studied had approval ratings above 50 percent: Narendra Modi of India, Alain Berset of Switzerland, Andrés Manuel López Obrador of Mexico and Anthony Albanese of Australia. Mr. Modi, who is in Hiroshima as an observer, is the envy of the town with a 78 percent approval score, though this is in a country where religious divisions are exploited for political gain and the prime minister’s top political opponent was kicked out of Parliament for defamation.

No G7 leader, by contrast, could muster the support of a majority. Prime Minister Giorgia Meloni of Italy, elected just last fall, fared best with a 49 percent approval rating, according to Morning Consult, followed by Mr. Biden with 42 percent, Prime Minister Justin Trudeau of Canada with 39 percent, Chancellor Olaf Scholz of Germany with 34 percent, Prime Minister Rishi Sunak of Britain with 33 percent and Prime Minister Fumio Kishida of Japan with 31 percent. President Emmanuel Macron of France trailed the pack with a dismal 25 percent.

Mr. Kishida managed to do better with the approval rating of his cabinet, which hit 52 percent in a recent poll. That was the first time it surpassed 50 percent in eight months, fueling speculation that he may call a snap election to take advantage while he’s ahead. But it was unclear whether the new poll was the beginning of a period of more sustained support, or just an aberration before he slides again.

“My instinct is the low polling numbers are more a reflection of growing polarization in a number of these societies,” said Michael Abramowitz, president of Freedom House, a Washington-based organization that encourages democracy around the world. “Biden could be paving the streets with gold and half the country would disapprove. Obviously, democracies need to do a better job, but there’s little evidence that authoritarians can do a better job.”

The disenchantment toward the current leadership is proving to be a test of the staying power of democracy at a time when it has come under pressure. Mr. Abramowitz’s group, which tracks democracy nation by nation, has found that freedom has retreated around the world 17 years in a row, amid rollbacks in places like Hungary and Poland. While former President Donald J. Trump has called for “termination” of the U.S. Constitution to return him to power, Mr. Biden often says that he sees his mission as defending democracy.

Amid the general sourness, each leader is confronting distinct problems. Mr. Macron, who won re-election just last year with 58.5 percent of the vote, saw his support plummet when he pushed through an increase in the retirement age to 64 from 62, touching off violent street protests. A poll released this month found that Mr. Macron would lose a rematch to Marine Le Pen, the far-right leader he defeated last year.

Likewise, if elections were held now, recent surveys show that Mr. Sunak’s Conservative Party would lose to the Labour Party in Britain, Mr. Trudeau’s Liberal Party would lose to the Conservative Party in Canada, and Mr. Scholz’s Social Democratic Party would lose to the Christian Democratic Union in Germany.

Some political veterans attribute the weakness of the G7 leaders to economic anxiety following the Covid-19 pandemic. “There seems to be a wave of dissatisfaction sweeping our democracies,” said Carl Bildt, a former prime minister of Sweden. “I think the return of inflation, long gone, might have something to do with this.”

Inflation has certainly sapped support for Mr. Biden, along with the crisis at the southwestern border, fear of urban crime, anger over government spending and concerns over the president’s age as he asks voters to give him a second term keeping him in power until he is 86.

The best thing Mr. Biden has going for him politically at the moment is the likelihood that he might face Mr. Trump again next year, a rematch that his strategists assume would galvanize Democrats and independents who are not enthusiastic about the president but are inexorably opposed to the former president. Even so, according to polls, it is not a given that the president can beat his predecessor a second time, and Mr. Biden’s peers in Japan are deeply worried about a Trump return to power, remembering him as a disruptive, even dangerous, force.

This is not the first time the Group of 7 has gathered with its leaders underwater politically at home. But John J. Kirton, director of the G7 Research Group at the University of Toronto and a longtime student of the bloc, said such fallow periods typically happen when the leaders’ home countries are afflicted by severe recessions or stagflation, which is not the case now.

“At such low-in-the-polls times, the G7 summit becomes the ultimate lonely hearts club, when the leaders share their political pain, bond with one another because of it, and discuss what is working in each country to get it and perhaps them back on track,” Mr. Kirton said. “This is one way that the summit serves as the committee to re-elect the existing leaders back home.”

But Mr. Abramowitz argued that the political troubles of the G7 leaders should be taken as proof that democracy works. “Unlike authoritarian leaders, if democratic leaders don’t get the job done, they’ll be voted out,” he said. “Accountability is a strength of democracies, not a weakness.”