Twenty one out of the 29 fatalities were registered in Odisha's town of Puri, where the storm caused a landfall, the NDTV broadcaster specified, citing Odisha Chief Secretary Aditya Prasad Padhi.
The death toll previously stood at 16 people.
The Indian government launched large-scale restoration work across 10,000 villages and 52 urban areas affected by Fani, the broadcaster added.
Odisha Chief Minister Naveen Patnaik announced on Sunday a relief package for the affected Indians, including cash, rice and polythene sheets.
READ MORE: Powerful Cyclone Fani Kills Almost 30 People in India, Bangladesh — Reports
After passing through Odisha, Fani started moving northward along the eastern coast of Hindustan and entered Bangladesh, where the death toll currently stands at 14 people.
Experts have qualified Fani as one of the most devastating cyclones that India saw over the past 20 years and the most powerful cyclone in Odisha since 2014. The cyclone has weakened into a "deep depression".