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Health ministry data from the world's second-most populous country showed more than 23,000 new cases on Monday, down slightly from Sunday's record increase of almost 25,000.
There have been almost 20,000 deaths in India since the first case was detected there in January.
India now trails only the United States and Brazil in the number of Covid-19 cases and it has recorded eight times as many cases as China, where the virus was first identified in late 2019.
But its death rate per 10,000 people is still a low 0.15, compared with 3.97 in the United States and 6.65 in the United Kingdom, according to a Reuters tally. Mainland China stands at 0.03.
Officials said they had reversed a decision to reopen the Taj Mahal, India's most famous tourist attraction, in the city of Agra, on Monday, following a rise in new cases in the area.
Some other monuments in and around the capital New Delhi opened on Monday, albeit with very few visitors. India is pushing ahead with relaxations to its more than two-month lockdown amid grim economic forecasts.
New Delhi, along with Maharashtra, home to India's financial capital Mumbai, and the southern state of Tamil Nadu account for about 60% of the total coronavirus cases in the country.
Maharashtra - the worst-hit state with nearly 210,000 cases - said it would let hotels outside containment zones reopen at 33% capacity from Wednesday and issued guidelines for staff and guests.
India is also seeing an uptake in cases in states such as Kerala, Karnataka and Assam, which until recently had been relatively unscathed.
"This is showing up as an urban health challenge," said Dr Rajib Dasgupta, a professor of community health at the Jawaharlal Nehru University in New Delhi, noting it is exposing weaknesses in the public health system.