Countries, companies and powerful members of the diaspora have all pledged to pitch in, but it likely won’t be enough to stop the unfolding catastrophe.NEW DELHI — Oxygen generators from Saudi Arabia and the United Arab Emirates. Raw material for coronavirus vaccines from the United States. Millions in cash from companies led by Indian-American businessmen.As a second wave of the pandemic rages in India, the world is coming to the rescue.But it is unlikely to plug enough holes in India’s sinking health care system to fully stop the deadly crisis that is underway, and the health emergency has global implications for new infections worldwide, as well as for countries relying on India for the AstraZeneca vaccine.“It’s a desperate situation out there,” said Dr. Ramanan Laxminarayan, the founder and director of the Center for Disease Dynamics, Economics & Policy, adding that donations will be welcome, but may only make a “limited dent on the problem.”In the early months of 2021, the government of Prime Minister Narendra Modi acted as if the coronavirus battle had been won, holding huge campaign rallies and permitting thousands to gather for a Hindu religious festival.Now, Mr. Modi is striking a far more sober tone. He said in a nationwide radio address on Sunday that India has been “shaken” by a “storm.”Patients are suffocating in the capital, New Delhi, and other cities because hospitals’ oxygen supplies have run out. Frantic relatives have appealed on social media for leads on intensive-care unit beds and experimental drugs. Funeral pyres have spilled over into parking lots and city parks.Now, Mr. Modi appears to be looking to the rest of the world to help India quell its seemingly unstoppable coronavirus wave.A global coronavirus surge, largely driven by the devastation in India, continues to break daily records and run rampant in much of the world, even as vaccinations steadily ramp up in wealthy countries. More than one billion shots have now been given globally.On Sunday, the world’s seven-day average of new cases hit 774,404, according to a New York Times database, higher than the peak average during the last global surge, in January. Despite the number of shots given around the world, far too few of the global population of nearly eight billion have been vaccinated to slow the virus’s steady spread.Vaccinations have been highly concentrated in wealthy nations: 82 percent of shots worldwide have been given in high- and upper-middle-income countries, according to data compiled by the Our World in Data project. Only 0.2 percent of doses have been administered in low-income countries.On Monday, India broke the world record for daily coronavirus infections for a fifth consecutive day, reporting nearly 353,000 new cases. And it added 2,812 deaths to its overall toll of more than 195,000, which experts say may be a vast undercount.Relatives of Covid-19 victims perform last rites in Delhi on Saturday.Atul Loke for The New York TimesEarlier this month, Adar Poonawalla, the chief executive of the Serum Institute of India, the world’s largest vaccine maker, made a direct appeal to President Biden on Twitter, asking him to “lift the embargo” on raw material used to make Covid-19 vaccines.Tim Manning, the White House Covid-19 supply coordinator, said that the U.S. Defense Production Act, which Mr. Biden invoked in March, did not equate to an embargo. “There are literally no export controls, export restrictions on vaccine inputs out of the United States,” Mr. Manning said.“The challenge,” he said, “what is actually happening globally, is that there is just a dramatically outstripped demand against the infrastructure for supply. And it’s really just that simple.”Facing increased pressure, the White House said Sunday that it had removed impediments to the export of raw materials for vaccines and would also supply India with therapeutics, test kits, ventilators and personal protective gear.“Just as India sent assistance to the United States as our hospitals were strained early in the pandemic, we are determined to help India in its time of need,” Mr. Biden said on Twitter.The Biden administration then said Monday that it would share up to 60 million AstraZeneca doses from its stockpile with other countries in the coming months, so long as they clear a safety review being conducted by the Food and Drug Administration.The U.S. surgeon general, Dr. Vivek Murthy, who announced the plan on Twitter, did not specify which countries would receive those doses.Members of Congress had lobbied Mr. Biden to donate the AstraZeneca vaccine to India, since there is no shortage for Americans who want to be vaccinated with the three vaccines that have been authorized for emergency use there.The extent of support the president offers India could lay the foundation for a Biden-Modi relationship at a time when the United States and China are both jockeying for influence with India and greater access to its enormous market.Mr. Biden’s response to India at its time of crisis has come under scrutiny, raising questions of how far the administration has actually moved away from former President Donald J. Trump’s “America First” foreign policies.The Serum Institute did not respond to questions about the White House’s announcement.Between bouts of the pandemic, when Mr. Modi’s government thought the worst was behind it, India enacted a policy of vaccine diplomacy, selling or donating 66.4 million doses.In late March as the domestic caseload began to creep upward, Mr. Modi suddenly stopped exports, crippling the vaccination campaigns of other countries reliant on made-in-India vaccine.The Indian government is now holding back nearly all of the 2.4 million doses produced daily by the Serum Institute, one of the world’s largest producers of the AstraZeneca vaccine. So far, only the U.S. has offered to fill some of the shortage.Still, vaccine shortages have hobbled India’s effort to protect its people. Only about 2 percent of the population has been fully inoculated.Signs indicating a shortage of vaccines in Mumbai last week.Francis Mascarenhas/ReutersSeveral other countries have also stepped up to offer support to India.Britain pledged medical equipment, including 495 oxygen concentrators (devices that can extract oxygen from ambient air and provide it to patients) and 140 ventilators. France and Australia are considering sending oxygen supplies. Even Pakistan, with which India has fought several wars and maintains chilly relations, has offered X-ray machines, ventilators and other aid, its foreign minister, Shah Mahmood Qureshi, said.Two Indian-American businessmen — the chief executive of Microsoft, Satya Nadella, and the Google chief, Sundar Pichai — have both said that their companies will provide financial assistance to India.“Devastated to see the worsening Covid crisis in India,” Mr. Pichai wrote on Twitter, pledging $18 million to aid groups working in the country.Indian officials have also been making direct requests of other countries. Subrahmanyam Jaishankar, India’s external affairs minister, tweeted last week about his meeting with Margrethe Vestager, the European Commission executive vice president who oversees digital policy. On Sunday, the European Union announced that it would provide oxygen and medicines.“The E.U. is pooling resources to respond rapidly to India’s request for assistance via the E.U. Civil Protection Mechanism,” Ursula von der Leyen, the president of the European Commission, said on Twitter.Mr. Jaishankar’s spokesman did not respond to a request for comment on the assistance promised to India, but experts said it could only do so much.Prime Minister Narendra Modi speaking in Ahmedabad in March.Amit Dave/ReutersIn many cases, India has lagged behind other countries with its preparedness measures and ability to scale up care, triaging resources like oxygen that reach patients just in time or not at all.“Early and aggressive investments were absolutely necessary,” said Krishna Udayakumar, an associate professor of global health and director of the Duke Global Health Innovation Center.Unlike the United States and Britain, which signed advance purchase agreements for millions of doses of the AstraZeneca vaccine beginning last May, India waited until January, and then only bought 15.5 million doses produced by Serum and the pharmaceutical company Bharat Biotech — a drop in the ocean for a country of nearly 1.4 billion people.India had indicated as early as last September, at the height of the first wave, that it would rely heavily on Russia’s Sputnik V vaccine, signing a deal to buy 100 million doses. But Sputnik won’t be available in India until next month at the earliest.If India were to dramatically ramp up its vaccine manufacturing capacity and give emergency authorization to other vaccine makers, it could potentially curb the worst effects of the second wave.“This is the only long-term solution,” Dr. Laxminarayan said. “India has the capability to do it, if the country puts its mind to it.”Rebecca Robbins contributed reporting.