NEW DELHI — Adar Poonawalla made big promises. The 40-year-old chief of the world’s largest vaccine maker pledged to take a leading role in the global effort to inoculate the poor against Covid-19. His India-based empire signed deals worth hundreds of millions of dollars to make and export doses to suffering countries.

Those promises have fallen apart. India, engulfed in a coronavirus second wave, is laying claim to his vaccines. Other countries and aid groups are now racing to find scarce doses elsewhere.