Public-health officials and leaders in developing-world countries are expected to press the Group of Seven countries to commit to large donations of Covid-19 vaccines and billions in financing at a summit later this week, saying the developing world needs more help to emerge from the worst of the pandemic.

High vaccination rates are helping wealthier nations recover from the health crisis, with coronavirus case numbers falling sharply and economies bouncing back.

But even as rich countries begin vaccinating low-risk people such as teenagers, many poor countries are far behind in their inoculation efforts, hobbling their economies and raising the risk that those regions could spawn more dangerous variants of the virus.

A number of rich countries, including the U.S., have pledged tens of millions of doses for poor nations. Nonetheless, pressure is building on the leaders of the G-7, which comprises Canada, France, Germany, Italy, Japan, the U.K. and the U.S., to commit to doing more at a summit starting Friday in the U.K.

Officials in developing countries, as well as public-health authorities, are calling on G-7 leaders to donate millions of shots to bridge a perilous supply gap over the summer and keep vaccine rollouts from stalling altogether.

“This is the most important G-7 in history, because this one can dictate how fast we can get out of this pandemic, and whether we save trillions of dollars and millions of lives,” said Bruce Aylward, senior adviser to the director general of the World Health Organization and leader of a partnership of international health groups, including the WHO, that are working together to overcome the pandemic.

The International Monetary Fund has proposed that rich countries donate 250 million doses to poor countries this summer to keep vaccination programs on track. Moreover, donations of an additional 750 million doses this year—shots the IMF calculates rich countries can spare without harming their own vaccination programs—could help poor countries inoculate 40% of their populations by the end of 2021.

The IMF, whose proposal is backed by the WHO, the World Trade Organization and the World Bank, also proposes that rich countries and multilateral organizations provide about $50 billion in financing to support vaccine campaigns.

Such support could increase global economic output by some $9 trillion by 2025, said Gita Gopinath, the IMF’s chief economist. “The important thing for the G-7 to recognize is that the window to realize these gains is closing very, very quickly. Action is needed now,” Ms. Gopinath said.

G-7 health ministers met at Oxford University last week ahead of the organization’s coming summit in the U.K.

G-7 health ministers met at Oxford University last week ahead of the organization’s coming summit in the U.K.

Photo: Steve Parsons/Press Pool

South Africa President Cyril Ramaphosa will attend the G-7 meeting to discuss Covid-19 support for poor countries. Indian Prime Minister Narendra Modi has been invited to attend in person, but a devastating Covid-19 surge in India will keep him at home. His office said he plans to participate virtually.

Messrs. Ramaphosa and Modi have also asked rich countries for funding and political support to build up vaccine-manufacturing capacities in developing nations to assure a supply of booster shots to counter emerging virus variants.

The Covax initiative, a WHO-supported program to distribute vaccines to developing countries, is facing “a huge hole” in supply between now and September, Mr. Aylward said. In the autumn, he expects vaccine deliveries to pick up, including from Covax’s main supplier in India, which has banned vaccine exports to divert the shots to its own population. If the immediate gap isn’t covered, “then we all have a problem,” he said.

So far, Covax has delivered 81 million doses to 129 countries, far short of the 238 million targeted by the end of May and its goal of 1.8 billion shots by early next year—a total that would cover 30% of the population of developing countries.

“ ‘This is the most important G-7 in history, because this one can dictate how fast we can get out of this pandemic, and whether we save trillions of dollars and millions of lives.’ ”

— Bruce Aylward, senior adviser to the World Health Organization’s director general

Rich nations have bought enough doses to immunize their populations multiple times over, a purchasing strategy that has made it difficult for Covax and poor countries to secure supplies. By the start of this week, high-income countries had administered 69 times more vaccine doses per capita than the lowest-income countries, according to the WHO.

The U.S. has pledged to share 80 million shots by the end of June, but hasn’t announced any further donations. The European Union has said it would give at least 100 million doses by the end of the year, without specifying when. Other G-7 members, including the U.K., have said they are ready to give away surplus supplies, but often without setting a timeline.

The U.S. has bought four doses per person, the EU seven and the U.K. more than eight, according to Duke University.

In a tweet posted after a meeting of G-7 health ministers last week, India’s health minister, Harsh Vardhan, urged support for the mantra of “Leave No One Behind.”

Messrs. Modi and Ramaphosa also intend to use the summit to lobby for support for a waiver of the intellectual property underlying Covid-19 vaccines. That initiative has won the support of the U.S., but not other G-7 members.

The summit is “an important opportunity to seek broader support for the struggle we are waging alongside India and more than 100 other countries,” Mr. Ramaphosa wrote in a weekly newsletter published Monday.

But at this week’s summit, those demands could collide with pressing domestic issues in many of the G-7 countries. Governments are racing to immunize as many of their citizens as possible ahead of the summer holidays, when travel rules are set to ease. There is also pressure to inoculate teenagers ahead of the start of the new school year in September, to allow for in-person learning.

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India has put vaccine distribution to other countries on hold as the country battles the world’s fastest-growing Covid-19 surge. The delay in distribution is hampering the global vaccination effort. Photo illustration: Laura Kammermann The Wall Street Journal Interactive Edition

More contagious new variants, including one discovered in India that is now driving up infections in the U.K., are endangering reopening plans and prompting governments to hold on to doses for potential booster shots. This could leave developing countries with vaccines to cover 10% of their population this year, the IMF analysis shows.

In Germany, Chancellor Angela Merkel’s party has come under criticism for the slow start of the country’s rollout earlier this year. Japan has fully immunized slightly more than 3% of its citizens, according to Our World in Data, a project based at Oxford University.

The shortage of vaccines has prevented developing nations from building up the infrastructure and public-information campaigns needed to get the shots into arms, Mr. Aylward said.

Some African countries are now considering stretching the interval between the first and second dose of the vaccine developed by AstraZeneca PLC to 16 weeks from the recommended 12—a strategy that hasn’t been tested in clinical trials. Others are preparing to substitute the second dose with another vaccine, including a much more expensive shot from Pfizer Inc. or Johnson & Johnson’s one-dose vaccine.

Meanwhile, some poorer nations, such as Pakistan, have instead sought vaccine supply from China, which isn’t a member of the G-7.

Write to Saeed Shah at saeed.shah@wsj.com and Gabriele Steinhauser at gabriele.steinhauser@wsj.com