KANPUR, India—Since losing his wife during a wave of the coronavirus last year, Ram Bilas Kovind said, he has been turned away repeatedly by authorities in the northern Indian city of Kanpur as he has unsuccessfully sought compensation available to India’s Covid-19 victims.

“They ask us for proof. How can we prove when she wasn’t tested, when she wasn’t hospitalized? Almost everyone in the area was sick at the same time,” said the 69-year-old. “We have nothing.”

Over the recent festival season in October, the darkest days of the pandemic seemed a distant memory. India’s authorities lifted a mask mandate for air travel, people flocked to markets to shop for Diwali gifts, and hotels prepared for large celebrations this wedding season. But not everyone has been able to move on from India’s brutal Covid-19 waves, and in particular the traumatic spring of 2021, when the highly contagious Delta variant of the coronavirus overwhelmed the hospital system.

Families struggled to get hospital beds and oxygen for their loved ones. As the number of deaths soared, cremation grounds ran out of room, and some families resorted to putting their dead into rivers. Many families are still reeling from the loss of loved ones during the pandemic and some, such as Mr. Kovind, are still waiting to be counted as part of its toll.

In Kanpur, northern India, where many families are still suffering from the loss of loved ones during the pandemic, some still wait to be counted as part of its toll.

In June 2021, India’s Supreme Court ordered the government to pay compensation to families of people who died of Covid-19, in a ruling on two public-interest petitions, and directed the national disaster agency to come up with a process. The court later approved a plan to pay families 50,000 rupees ($605), a significant sum for many in India, to be paid by the states. India’s health ministry issued guidelines for compensation claims—such as that the death should have happened within a month of being diagnosed with Covid.

Mr. Kovind said compensation for his wife’s death would validate the painful experiences he went through. Payment “is important—not just financially, but also emotionally,” he said. “It would be a reassurance that Munni’s death has been acknowledged.”

The World Health Organization has estimated that India saw 4.7 million more deaths than should have been expected between early 2020, when the pandemic began its global spread, until the end of 2021. That is about 10 times the official Indian Covid-19 death toll for that period. The agency attributes these excess deaths both directly to Covid-19 and to people not being able to access healthcare for other conditions.

India has disputed those numbers, saying it disagreed with the methodology used to arrive at the estimate. It has said that more than half a million people have died in India of Covid-19 since the start of the pandemic.

Public-health researchers say that few countries adequately captured the pandemic’s true toll as it unfolded and that a comprehensive understanding of Covid-19’s effects on mortality remains vital for India’s health programs.

“Despite India’s young demographic, mortality was staggeringly high. In fact, our study showed that there were weeks—even before the peak—that excess mortality was among the highest in the world,” said Satchit Balsari, assistant professor of emergency medicine at Harvard Medical School, and one of the authors of a study published in August that examined excess deaths in the state of Gujarat during the pandemic. “Without knowing who died, and why, how is India to know what to fix?”

Ram Bilas Kovind, at his house in Kanpur, said payment would be a reassurance that his wife’s death has been acknowledged.

A crematorium in New Delhi in April 2021. Few countries adequately captured the pandemic’s true toll as it unfolded, researchers say.

Photo: DANISH SIDDIQUI/REUTERS

India’s health system can struggle to meet the needs of its more than 1.3 billion people even during normal times, given the relatively low numbers of hospitals and medical staff it presently counts on.

The health ministry didn’t reply to a request for comment. 

The country’s junior health minister told Parliament in March, in response to a question on the accuracy of India’s Covid-19 death toll, that the government had issued detailed guidelines to states on how to record Covid-19 deaths, and that state authorities regularly reconcile and update these numbers. The official toll is the total of data provided by the country’s states.

“At times, certain reports have speculated excess deaths higher than the official number of Covid-19 fatalities officially reported by India,” said Dr. Bharati Pravin Pawar, the minister of state in India’s Ministry of Health and Family Welfare. “These reports have mostly relied on unvalidated methodologies, or the data sources used to derive ‘estimates’ aren’t reliable.”

A Wall Street Journal comparison of death records for 2019, just before the pandemic, and 2020 and 2021 obtained from Kanpur and Mumbai, two of India’s largest cities, showed sharp increases in the number of deaths recorded in the worst months for Covid-19 outbreaks in the two pandemic years.

Kanpur, a city of about three million people in northern Uttar Pradesh state, recorded nearly 29,000 deaths last year, almost 11,000 more than the total deaths recorded in 2019, according to city data obtained by the Journal. Nearly 4,600 people died in the city in May alone, according to official city figures, three times the number in the same month in 2019.

Officially, the city attributed only 1,166 deaths to Covid-19 in 2021 and 739 in the previous year. There were more deaths counted in just two months by the city’s main crematorium, Bhairav Ghat, where records showed 2,176 Covid-19 cremations in April and May last year.

City and state authorities didn’t respond to requests for comment.

A Covid-19 testing site in Mumbai in 2021. India’s health system can struggle to meet the needs of its more than 1.3 billion people even during normal times.

Photo: Dhiraj Singh/Bloomberg News

Even in India’s financial capital, Mumbai, in the western state of Maharashtra, where city health officials say they have almost 100% registration of deaths, among the most complete in the country, a Journal analysis suggests a gap between excess deaths and those officially attributed to Covid-19.

In 2021, the number of deaths in Mumbai was 13,500 higher than in 2019, according to the Journal’s analysis of city data. But Mumbai said it had only 7,009 Covid-19 deaths that year. In April alone, more than 15,000 residents died, more than double the number in the same month before the pandemic.

Mumbai health officials said the discrepancy between the official Covid-19 toll and the number of excess deaths is due to deaths indirectly related to the pandemic, such as people who were unable to get treatment for other health conditions. “The excess deaths numbers reflect the broader impact of Covid-19,” said the Mumbai public health department, adding that further study of those deaths was needed.

It was the middle of April in 2021 when Mr. Kovind’s wife, Munni Devi, began running a fever and feeling aches and pains. A little over a week later, the 55-year-old was struggling for breath, he said.

He tried to take her to multiple hospitals, but said they were repeatedly turned away by hospital staff, who cited a lack of beds and Covid-19 tests. Patients were even lying on the floors of hospitals, he said. At one private hospital, a doctor said she “looked like a suspected Covid case, but he had no way to be sure,” Mr. Kovind said.

Mr. Kovind ended up treating his wife at home with herbal remedies and waited for help to come from an official helpline. “No one turned up. She died before a test could be done,” he said.

The court has said that, in addition to a death certificate listing Covid-19, or a PCR or rapid antigen test, medical investigations in a hospital setting that pointed to a Covid-19 infection would also suffice as evidence for compensation, and the families of Covid patients who died at home are also eligible for compensation. But none of this helps Mr. Kovind, who said he hasn’t been able to obtain a death certificate for his wife, as he lacks the necessary documents.

According to information provided by the government to India’s parliament in August, some 791,353 claims for Covid-19 compensation were approved as of May, using broader criteria for determining approval laid down by the top court.

Mohd. Qamruddin, supervisor of the Bhairav Ghat crematorium, inspects electric furnaces that were used to cremate bodies of people who died from Covid-19.

Bhairav Ghat was the designated crematorium for Covid deaths in Kanpur during India’s second wave. Bodies were burned in furnaces or on pyres along the Ganges.

Mumbai resident Atmaram Parshuram Sogam, 71, said he is among those whose claim wasn’t approved. He and his wife fell ill with fevers in early June 2020, and her condition began to deteriorate rapidly, Mr. Sogam said. “She couldn’t eat; she was so weak,” he said.

Arti Sogam, 60, was first taken by Mr. Sogam to a nearby private hospital, but they denied her admission without a Covid-19 test report, he said. He said he then took her to a municipal hospital designated for Covid-19 care. One of their daughters went to see her mother the night she was admitted. Through a window, she could see that Ms. Sogam was on a ventilator, Mr. Sogam said. 

Ms. Sogam died the following night. The hospital marked her death as “suspected Covid,” according to the hospital’s medical certification of cause of death provided to the family and seen by the Journal, meaning she had Covid-19 symptoms but no test to confirm the infection.

Ms. Sogam’s body was taken directly from the hospital to one of the largest municipal cremation grounds in Mumbai. Under Covid-19 protocols, Mr. Sogam was allowed to go only as far as the crematorium’s gates. The ambulance staff, wearing protective suits, helped cremate Ms. Sogam’s body.

“Her body was wrapped in white sheets. I couldn’t see her face even for the last time,” Mr. Sogam said, his voice choking and eyes brimming with tears. “The way they handed over her body, I assume she must have died due to Covid.”

About 12,000 people died in the city the same month, according to the Mumbai public-health department, about 5,000 more than in June of 2019.

For months in 2021, Mr. Sogam, a retired salesman, made the rounds of hospital and government offices to establish that his wife died of Covid-19. The hospital where his wife died told him it had no record of a Covid-19 test for her, he said. Municipal officials in Mumbai and state officials also told him they don’t have his wife’s name in their official Covid-19 count, Mr. Sogam said.

In many states that experienced severe Covid-19 waves in 2021, the number of applications for compensation has been far higher than the official toll, according to information the states provided to the Supreme Court. In the state of Gujarat, for example, the number of claims applications was nine times the official Covid-19 toll as of January 2022.

After more than a year of trying, many families have lost hope of getting the compensation that would make a huge difference to their lives. The money is as much as Mr. Kovind’s son earns in six months as a stone polisher at a construction site. Mr. Kovind no longer works. The family has been relying on a government grain program expanded during Covid-19 to be able to eat two meals a day. “We are patiently waiting that God might be kind with us,” he said.

Ram Bilas Kovind holding a photograph of himself with his wife, Munni Devi.

Write to Vibhuti Agarwal at vibhuti.agarwal@wsj.com and Krishna Pokharel at krishna.pokharel@wsj.com