The Indian vaccine giant expected to supply much of the world warns that it has been directed to put its country’s needs ahead of exports.

The chief executive of the Indian pharmaceutical giant that dozens of countries are counting on to supply them with Covid-19 vaccines said on Sunday that their deliveries might be delayed because it had been “directed” to fill domestic needs ahead of export orders.

“Dear countries & governments,” the executive, Adar Poonawalla of the Serum Institute of India, wrote in a tweet in which he warned of delays. “I humbly request you to please be patient,” he wrote, adding that his company had been directed to prioritize “the huge needs of India and along with that balance the needs of the rest of the world. We are trying our best.”

He did not say who had issued the directive, and the Serum Institute did not immediately return requests for comment.

India produces three-fifths of the world’s supply of all kinds of vaccines, and the country’s prime minister, Narendra Modi, has launched one of the world’s largest and most ambitious vaccination campaigns, aiming to inoculated India’s 1.3 billion people.

But even though the country already operates a huge immunization program, administering about 390 million shots against ailments like measles and tuberculosis in an average year, India is struggling to get Covid inoculations to the population. Less than 1 percent of Indians have been inoculated since mid-January. The pandemic has caused at least 10.9 million known coronavirus infections in India so far, more than in any other country except the United States.

The country’s regulators have approved two vaccines: one developed by AstraZeneca and Oxford University and produced by the Serum Institute, and another — still in trials — developed by the National Institute of Virology with Bharat Biotech, a local pharmaceutical company that will make the doses.

The Serum Institute will also make doses of a vaccine developed by Novovax once it is approved.

Besides helping supply India and other clients, the company is expected to produce hundreds of millions of doses of the AstraZeneca vaccine and more than a billion Novovax vaccines to be distributed through the global vaccination initiative Covax, which aims to ensure that 92 low- and middle-income countries receive vaccines at the same time as the world’s 98 richer countries. Covax did not immediately respond to requests for comment about Mr. Poonawalla’s alert that foreign countries would have to wait for vaccines.

Many developing countries want the AstraZeneca vaccine because it is much less expensive and much easier to store and transport than other Covid vaccines now in use. That also makes it suitable for India’s vast vaccination campaign, which must reach from the towering Himalayan mountains to South India’s dense jungles.

The Indian government has increasingly used the country’s vaccine manufacturing capacity as a currency for its international diplomacy, in competition with China, which has made doling out shots a central plank of its foreign relations. Last week, for example, India promised to donate 200,000 vaccine doses for United Nations peacekeepers around the world.