An ambitious effort by the World Health Organization to calculate the global death toll from the coronavirus pandemic has found that vastly more people died than previously believed — a total of about 15 million by the end of 2021, more than double the official total of six million reported by countries individually.

But the release of the staggering estimate — the result of more than a year of research and analysis by experts around the world and the most comprehensive look at the lethality of the pandemic to date — has been delayed for months because of objections from India, which disputes the calculation of how many of its citizens died and has tried to keep it from becoming public.

More than a third of the additional nine million deaths are estimated to have occurred in India, where the government of Prime Minister Narendra Modi has stood by its own count of about 520,000. The W.H.O. will show the country’s toll is at least four million, according to people familiar with the numbers who were not authorized to disclose them, which would give India the highest tally in the world, they said. The Times was unable to learn the estimates for other countries.

The W.H.O. calculation combined national data on reported deaths with new information from localities and household surveys, and with statistical models that aim to account for deaths that were missed. Most of the difference in the new global estimate represents previously uncounted deaths, the bulk of which were directly from Covid; the new number also includes indirect deaths, like those of people unable to access care for other ailments because of the pandemic.

The delay in releasing the figures is significant because the global data is essential for understanding how the pandemic has played out and what steps could mitigate a similar crisis in the future. It has created turmoil in the normally staid world of health statistics — a feud cloaked in anodyne language is playing out at the United Nations Statistical Commission, the world body that gathers health data, spurred by India’s refusal to cooperate.

“It’s important for global accounting and the moral obligation to those who have died, but also important very practically. If there are subsequent waves, then really understanding the death total is key to knowing if vaccination campaigns are working,” said Dr. Prabhat Jha, director of the Centre for Global Health Research in Toronto and a member of the expert working group supporting the W.H.O.’s excess death calculation. “And it’s important for accountability.”

To try to take the true measure of the pandemic’s impact, the W.H.O. assembled a collection of specialists including demographers, public health experts, statisticians and data scientists. The Technical Advisory Group, as it is known, has been collaborating across countries to try to piece together the most complete accounting of the pandemic dead.

The Times spoke with more than 10 people familiar with the data. The W.H.O. had planned to make the numbers public in January but the release has continually been pushed back.

Recently, a few members of the group warned the W.H.O. that if the organization did not release the figures, the experts would do so themselves, three people familiar with the matter said.

A W.H.O. spokeswoman, Amna Smailbegovic, told The Times, “We aim to publish in April.”

Dr. Samira Asma, the W.H.O.’s assistant director general for data, analytics and delivery for impact, who is helping to lead the calculation, said the release of the data has been “slightly delayed” but said it was “because we wanted to make sure everyone is consulted.”

India insists that the W.H.O.’s methodology is flawed. “India feels that the process was neither collaborative nor adequately representative,” the government said in a statement to the United Nations Statistical Commission in February. It also argued that the process did not “hold scientific rigor and rational scrutiny as expected from an organization of the stature of the World Health Organization.”

The Ministry of Health in New Delhi did not respond to requests for comment.

India is not alone in undercounting pandemic deaths: The new W.H.O. numbers also reflect undercounting in other populous countries such as Indonesia and Egypt.

Dr. Asma noted that many countries have struggled to accurately calculate the pandemic’s impact. Even in the most advanced countries, she said, “I think when you look under the hood, it is challenging.” At the start of the pandemic there were significant disparities in how quickly different U.S. states were reporting deaths, she said, and some were still collecting the data via fax.

India brought a large team to review the W.H.O. data analysis, she said, and the agency was glad to have them do it, because it wanted the model to be as transparent as possible.

India’s work on vaccination has won praise from experts globally, but its public health response to Covid has been criticized for overconfidence. Mr. Modi boasted in January 2021 that India had “saved humanity from a big disaster.” A couple of months later, his health minister declared that the country was “in the endgame of Covid-19.” Complacency set in, leading to missteps and attempts by officials to silence critical voices within elite institutions.

Science in India has been increasingly politicized over the course of the pandemic. In February, India’s junior health minister criticized a study published in the journal Science that estimated the country’s Covid death toll to be six to seven times greater than the official number. In March, the government questioned the methodology of a study published in The Lancet that estimated India’s deaths at four million.

“Personally, I have always felt that science has to be responded with science,” said Bhramar Mukherjee, a professor of biostatistics at the University of Michigan School of Public Health who has been working with the W.H.O. to review the data. “If you have an alternative estimate, which is through rigorous science, you should just produce it. You cannot just say, ‘I am not going to accept it’.”

India has not submitted its total mortality data to the W.H.O. for the past two years, but the organization’s researchers have used numbers gathered from at least 12 states, including Andhra Pradesh, Chhattisgarh and Karnataka, which experts say show at least four to five times more deaths as a result of Covid-19.

Jon Wakefield, a professor of statistics and biostatistics at the University of Washington who played a key role in building the model used for the estimates, said an initial presentation of the W.H.O. global data was ready in December.

“But then India was unhappy with the estimates. So then we’ve subsequently done all sorts of sensitivity analyses, the paper’s actually a lot better because of this wait, because we’ve gone overboard in terms of model checks and doing as much as we possibly can given the data that’s available,” Dr. Wakefield said. “And we’re ready to go.”

The numbers represent what statisticians and researchers call “excess mortality” — the difference between all deaths that occurred and those that would have been expected to occur under normal circumstances. The W.H.O.’s calculations include those deaths directly from Covid, deaths of people because of conditions complicated by Covid, and deaths of those who did not have Covid but needed treatment they could not get because of the pandemic. The calculations also take into account expected deaths that did not occur because of Covid restrictions, such as those from traffic accidents.

Calculating excess deaths globally is a complex task. Some countries have closely tracked mortality data and supplied it promptly to the W.H.O. Others have supplied only partial data, and the agency has had to use modeling to round out the picture. And then there is a large number of countries, including nearly all of those in sub-Saharan Africa, that do not collect death data and for which the statisticians have had to rely entirely on modeling.

Dr. Asma of the W.H.O. noted that nine out of 10 deaths in Africa, and six out of 10 globally, are not registered, and more than half the countries in the world do not collect accurate causes of death. That means that even the starting point for this kind of analysis is a “guesstimate,” she said. “We have to be humble about it, and say we don’t know what we don’t know.”

To produce mortality estimates for countries with partial or no death data, the experts in the advisory group used statistical models and made predictions based on country-specific information such as containment measures, historical rates of disease, temperature and demographics to assemble national figures and, from there, regional and global estimates.

Besides India, there are other large countries where the data is also uncertain.

Russia’s ministry of health had reported 300,000 Covid deaths by the end of 2021, and that was the number the government gave the W.H.O. But the Russian national statistics agency that is fairly independent of the government found excess mortality of more than one million people — a figure that is reportedly close to the one in the W.H.O. draft. Russia has objected to that number, but it has made no effort to stall the release of the data, members of the group said.

China, where the pandemic began, does not publicly release mortality data, and some experts have raised questions about underreporting of deaths, especially at the beginning of the outbreak. China has officially reported fewer than 5,000 deaths from the virus.

While China has indeed kept caseloads at much lower levels than most countries, it has done so in part through some of the world’s strictest lockdowns — which have had their own impact on public health. One of the few studies to examine China’s excess mortality using internal data, conducted by a group of government researchers, showed that deaths from heart disease and diabetes spiked in Wuhan during that city’s two-month lockdown. The researchers said the increase was most likely owing to inability or reluctance to seek help at hospitals. They concluded that the overall death rate in Wuhan was about 50 percent higher than expected in the first quarter of 2020.

India’s effort to stall the report’s release makes clear that pandemic data is a sensitive issue for the Modi government. “It is an unusual step,” said Anand Krishnan, a professor of community medicine at the All India Institute of Medical Sciences in New Delhi who has also been working with the W.H.O. to review the data. “I don’t remember a time when it has done so in the past.”

Ariel Karlinsky, an Israeli economist who built and maintains the World Mortality Dataset and who has been working with the W.H.O. on the figures, said they are challenging for governments when they show high excess deaths. “I think it’s very sensible for the people in power to fear these consequences.”

Vivian Wang contributed reporting.