Indian Prime Minister Narendra Modi was vaccinated against Covid-19 Monday, but a glitch in an online booking system meant thousands were turned away from hospitals across the country.

India's 11.1 million coronavirus case total is topped only by the United States.

The government -- which has set an ambitious target of vaccinating 300 million people by the end of June -- has opened up the jabs to all over-60s and any over-45s with serious illnesses.

Since the vaccination drive launched in January, only 14 million people have had jabs, mainly health workers and security forces.

Modi received a domestic developed vaccine, Covaxin, in a carefully choreographed operation at the AIIMS national medical institute.

The vaccine, developed by Bharat Biotech, is one of two approved for use in India even though the late stage data from trials on 25,800 volunteers have not yet been released.

Despite criticism from some doctors and health workers, India's drug regulator and the company insist it is safe for use.

Fears over vaccines have contributed to the slow pace of innoculation and Modi said on Twitter: "I appeal to all those who are eligible to take the vaccine. Together, let us make India COVID-19 free!"

Problems with online registration did not help on the first day of the new drive.

"It's utter chaos here," said Nilanjana Gupta, who took her lawyer father Sunil Gupta to the Max Smart Super Speciality hospital in Delhi.

Gupta said the administrators were "clueless". She said it took more than 30 attempts to get a registration number on the government app. "I expected this but it's still very frustrating," she added.

An uncle of US Vice-President Kamala Harris was also among those affected.

Balachandran Gopalan, an academic, told AFP he got onto the government portal and received a registration number and an appoinment at a hospital in New Delhi's Malviya Nagar area.

"Once I got there, they checked my registration details and said they have no record of it," the 79-year-old said.

Gopalan said hospital officials could not tell him when his turn would come. "I understand the doctors are stressed," he said. "But why put the patients under stress?"

Some, like 69-year-old Vijaya Shankar, were happy after they got the inoculation, which cost just $3.40.

"I have waited for so long and the day is now finally here. I think the government has done a great job," she said. "The vaccine is cheap, I dont mind paying."

Firhad Hakim, mayor of the eastern city of Kolkata, acknowledged "some technical glitches" but said the operation was generally going well.

"Security has been beefed up in and around hospitals to control the crowd," he said.

The vaccination drive has been stepped up as India sees a surge in new cases after a dramatic fall in recent months. New cases have risen to about 15,000 a day from about 10,000 a month ago.

New lockdown restrictions have been ordered in major cities in Maharashtra state, which has been India's worst hit in the pandemic.