India started vaccinating children aged 15 to 18 against the coronavirus on Monday as it expands its inoculation effort to protect the world's largest adolescent population.

Authorities on Monday reported 33,750 new Covid-19 cases and 123 deaths. The total number of cases of the fast-spreading Omicron variant detected in India was 1,700, the health ministry said.

Private and public schools will double up as vaccination centres for children and school authorities have been ordered to report their daily vaccination data to state authorities.

"Children are going to be given vaccines in their schools. They can also go to vaccination centres and get the dose ... they can just walk in," said Jai Prakash Shivahare, health commissioner in Gujarat state.

Several countries including the United States, Britain and South Korea have seen infections among children fuelling a rise in cases in recent weeks and have encouraged parents to get their children vaccinated.

Authorities in Gujarat, which is Prime Minister Narendra Modi's home state, are hoping to give a first dose to 3.6 million children this week.

"We have the capacity and we have the vaccines to cover most of the children. We appeal to parents to cooperate and ensure the children are vaccinated at the earliest," Shivahare said.

The UN children's agency UNICEF estimates India has the largest population of adolescents in the world with about 253 million of them.

Thousands of children, many accompanied by parents, queued up outside schools, medical centres and special health camps from early on Monday to secure their first dose of a vaccine.

"Some students are nervous to get their first shot but we're offering them some fruit and trying to keep them busy in the classrooms," said Fateh Singh Rawat, who heads a public school in Jaipur, capital of Rajasthan state.

The government is only giving children Bharat Biotech's Covaxin vaccine as that is the only vaccine with emergency use listing for the 15-18 age group, the health ministry said last week.

Adults in India get Covaxin, the AstraZeneca vaccine, which is branded as Covishield, and the Sputnik V shot.

The chief minister of Assam state said he hoped to see two million children vaccinated over the next week.

"Together we can fight Covid-19 and I am sure we're on the right track," said.