Its health ministry said 3,689 people had died within the past 24 hours.
Prime Minister Narendra Modi met the health minister on Sunday morning to review the crisis.
Hospitals are battling to treat patients amid a chronic shortage of beds and medical oxygen.
Amid the crisis, vote counting started on Sunday for elections held in four states: 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.
India has recorded more than 19 million cases of coronavirus - second only to the US. It has also confirmed more than 215,000 deaths, though the real toll is thought to be far higher.
Experts 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.