PUNE, India—At least five people were killed in a fire that broke out Thursday at a building under construction at Serum Institute of India, the world’s largest vaccine manufacturer, officials said. The company said the blaze would not affect production of the COVID-19 vaccine. Murlidhar Mohol, mayor of Pune city in southern Maharashtra state, said five bodies were found in the rubble after the flames were extinguished by firefighters. Mahol said the victims were probably construction workers. He said the cause of the fire had not been determined and the extent of damage was not immediately clear. Serum Institue of India’s CEO, Adar Poonwala, said he was “deeply saddened” by the loss of life. He said there would be no reduction in vaccine manufacturing because the company has other available facilities. The company said the fire was restricted to a new facility it is constructing to increase the production of …