NEW DELHI — Many Indian state leaders have asked Prime Minister Narendra Modi to open up vaccinations to most of the country’s hundreds of millions of adults, following a second surge in infections that has eclipsed the first wave.

India breached the grim milestone of 100,000 daily infections for the first time on Monday, and cases are likely to stay high again when fresh figures are released later on Tuesday.

The country, the world’s biggest vaccine maker, this month expanded its vaccination programme to include everyone above the age of 45. So far it has vaccinated only about 1 in 25 people, compared with nearly 1 in 2 in the United Kingdom and 1 in 3 in the United States.

“If a larger number of young and working population is vaccinated, the intensity of the cases would be much lower than the treatment that they need today,” Uddhav Thackeray, chief minister of India’s worst affected Maharashtra state, wrote in a letter to Mr. Modi late on Monday.

Delhi Chief Minister Arvind Kejriwal and many other states have also asked for faster and wider vaccinations, with some flagging tightness in vaccine supplies even for the prioritized groups.

The federal government has said it will widen the vaccination campaign in the “near future” to include more people, and that vaccine supplies are being stepped up.

With 12.6 million cases, India is the worst affected country after the United States and Brazil. Deaths have gone past the 165,000 mark.

The country’s daily infections have risen many fold since hitting a multi-month low in early February, when authorities eased most restrictions and people largely stopped wearing masks and following social distancing.

India has recorded the most number of infections in the past week anywhere in the world. More infectious variants of the virus may have played a role in the second surge, some epidemiologists say. — Reuters