Around 3,689 had died in one day, its health ministry said.
The nation’s health system has collapsed and hospitals are struggling to treat patients due to a chronic shortage of beds and medical oxygen.
Prime Minister Narendra Modi met his health minister on Sunday morning amid the major humanitarian crisis.
New variants have in part fuelled a surge in cases in India, where Covid-19 has claimed at least 215,000 lives.
More than 19 million cases of coronavirus have been recorded - second only to the US.
Foreign Secretary Dominic Raab has said the UK would “look very carefully” at any request for vaccines from India as the nation struggles to tackle the deadly wave.
He will meet with his Indian counterpart Subrahmanyam Jaishankar on Monday when he hosts face-to-face meetings with G7 foreign ministers.
Experts in India have cited low testing rates and the number of people dying at home, especially in rural areas, as contributing factors to under-reported figures.
The country’s previous highest daily death toll, also reported this week, was 3,645.
Brazil and the US have both registered daily tolls of more than 4,000 during the course of the pandemic.
Distressing images of families begging for hospital beds and life-saving supplies have been emerging for more than 10 days, while morgues and crematoriums remain overwhelmed.
Twelve people died on Saturday at Delhi’s Batra Hospital after it ran out of oxygen - for the second time in a week.
The Times of India newspaper reported 16 deaths in the southern state of Andhra Pradesh due to oxygen shortages in two hospitals, and six in the Delhi suburb of Gurgaon.
Delhi High Court has now declared it will start punishing officials if life-saving supplies don’t make it to hospitals.
Justices Vipin Sanghi and Rekha Patil said: “Water has gone above the head. Enough is enough.”
Amid the crisis, counting started on Sunday for elections held in the states of Assam, West Bengal, Tamil Nadu, and Kerala - and the union territory of Puducherry.
The outcomes are being watched for signs of how the pandemic has affected support for Mr Modi and his Hindu nationalist party, the BJP. He has been criticised for allowing rallies to take place during polling in March and April.
Results so far from West Bengal, where Mr Modi had been seeking a win, instead suggest the TMC party of fierce Modi critic Mamata Banerjee will comfortably retain power.
All adults in India are now eligible for a coronavirus vaccine.
But the planned launch of a nationwide drive on Saturday faltered as several states said they did not have enough doses to start vaccinating those aged 18-44.
Despite being the world’s largest producer of jabs, the country is suffering an internal shortage and has placed a temporary hold on all exports of AstraZeneca to meet domestic demand.
India has been using two vaccines, Oxford-AstraZeneca, known locally as Covishield, and another made by Indian firm Bharat Biotech, Covaxin.
The Russian-made Sputnik V vaccine has also been approved for use, and the first 150,000 doses arrived on Saturday.
The UK has sent shipments of oxygen concentrators and ventilators to Delhi, but the nation is in dire need of vaccines.
Mr Raab said the Government has not had a request for vaccines from Delhi as he was questioned over plans as Britain vaccinates younger and healthier people.
“We’ll always look very carefully at any requests we’ve got,” he told The Andrew Marr Show.
He said he was not going to “speculate on hypothetical scenarios” when pressed if ministers would grant India access to UK supplies.
“The Indian relationship is very important to us and we’d obviously want to co-operate very closely together,” Mr Raab said.
“You know, right throughout this crisis we have said we need to keep supply chains, particularly supply chains, open and we ought to resolve these kind of issues through collaboration, and that is certainly what we’re doing with the Indians.”
Labour shadow foreign secretary Lisa Nandy said Britain should aim to send jabs to India “as soon as possible” but that the UK programme should not be paused to do so.
“We haven’t defeated this virus in Britain yet and we need to keep up the momentum with that vaccination programme,” she told Marr on the BBC.
“This is a question that is really personal to me. I just found out last night that a close family member in India is in hospital with Covid and I’ve got family members here in the UK who are deeply affected by Covid as well.”
A UK order of five million AstraZeneca doses has been stalled in India over a need for re-testing and there have been questions over whether the Government may allow them to be used there.
Professor Peter Openshaw, a scientist who advises the Government, said it would be a “very reasonable arrangement” to allow India to keep those jabs.
But he added: “It’s a matter of balancing what we have available to our own population and what we can distribute equitably around the world through these well-organised systems that are in place.”