The figure includes 41 foreign nationals and seven deaths.
Gujarat, Bihar and Maharashtra reported a death each on Sunday. Four fatalities were reported earlier from Karnataka, Delhi, Maharashtra and Punjab, the ministry said.
The 415 figure also includes 24 people who have been cured, discharged or migrated, it said.
The Indian Council of Medical Research (ICMR) said 18,383 samples have been tested till 10 am on Monday.
It was not immediately clear where the new cases have come from.
The total number of positive novel coronavirus cases includes 67 in Maharashtra, including three foreigners, and Kerala also at 67, with seven foreign nationals, data issued by the ministry showed.
Till Monday morning, Delhi had reported 29 positive cases, including a foreigner, while Uttar Pradesh recorded 28, also including a foreigner, it added. Rajasthan reported 27 cases, of which two are foreigners. Telangana reported 26 cases, including 11 foreigners. Karnataka has 26 coronavirus patients, the ministry said.
Cases have been reported from across the country, including from Haryana, Punjab, Gujarat, Tamil Nadu, West Bengal, Andhra Pradesh and Uttarakhand.