Officials said that engineers were working to restore phone lines and power supplies that were cut off in some regions during the cyclone, while rail and air traffic had resumed normal service on Saturday.
The storm over the Bay of Bengal made landfall between Cuddalore in Tamil Nadu state and the federally administered territory of Pondicherry on Friday morning, the Indian Meteorological Department said.
Large areas were flooded, trees and power lines were uprooted and transportation was disrupted after heavy rains and winds with speeds up to 140 kilometres per hour.
Twenty-one people died in Cuddalore - either crushed under collapsed houses and fallen trees, or electrocuted by downed wires, officials told the IANS news agency.
Five people died in three other districts of Tamil Nadu, while seven people were killed in Pondicherry, which was cut off from neighbouring areas as trees blocked key highways.
Heavy rains also lashed Chennai, the capital of Tamil Nadu, about 180 kilometres north of Cuddalore.
Cuddalore was the worst-hit region as badly damaged roads made it difficult for disaster management teams to reach fishing villages. An estimated 5,000 fishermen homes were damaged in the region.
In Pondicherry, thatched huts and slums were destroyed.
"We don't know what is happening in the outside world. Even mobile phone signals are not proper. All we hear is the howling of fierce wind. Many trees have fallen down," Pondicherry resident S Ravikumar told IANS.
As 1.5-metre-high waves lashed the shore, fishermen were advised not to venture into the rough sea.
Train operations in the region were suspended, and thousands of people living in low-lying areas were evacuated to 49 cyclone shelters, IANS reported.
Crops on about 25,000 acres of land in the Cauvery delta region are estimated to have been damaged by the cyclonic winds.
Later Thursday, the meterological department withdrew its cyclone warning and said the storm had "weakened rapidly into a deep depression."
It warned, however, that there would be "heavy to very heavy" rains accompanied by fierce winds in parts of Tamil Nadu, Pondicherry, and the other southern states of Andhra Pradesh, Karnataka and Kerala until Saturday morning.
Cyclones that form frequently over the Bay of Bengal bring widespread destruction and flooding to India's southern and eastern coasts.
In 2010, 27 people died when Andhra Pradesh was battered by Cyclone Laila. More than 1,600 people were killed as storms hit Andhra Pradesh in November 1996.
Teams set up
The Tamil Nadu government has set up 20 teams to monitor the water levels in lakes and other water bodies in Chennai, Thiruvallur and other places. Eight teams of the National Disaster Management Force have been sent to the coastal districts.
Cuddalore district officials said traffic on the Cuddalore-Chidambaram road was suspended due to uprooting of trees.
In Puducherry, power has been switched off since 11pm on Thursday night as a precaution,.
Heavy rain, accompanied by a strong gale lashed south coastal Andhra and Chittoor district of Rayalaseema region under the impact of the cyclone. Parts of Nellore, Prakasam, Guntur and Chittoor districts have been receiving rain since morning.
Two villages of Kandriga block in Chittoor district have been inundated.
There were reports of strong gales uprooting trees in the coastal areas. High tidal waves continued to slam the coast. Sea water entered into houses near Suryalanka coast in Guntur district.
Chittoor, Tirupati and other towns in Chittoor district received heavy rain since early morning.
Jayalalitha allots Rs1.5 billion for relief work
South Indian state Tamil Nadu Chief Minister Jayalalitha yesterday alloted Rs1.5 billion (Dh100.76 million) for immediate relief measures and directed four ministers to visit the districts which bore the brunt of Cyclone Thane.
After chairing a meeting with senior department officials, Jayalalitha said she had asked her cabinet colleagues B.V. Ramana, T.K.M. Chinnaiah, K.A. Jeyapaul and M C Sampath to visit Kancheepuram, Villupuram, Nagapattinam and Cuddalore districts, the worst hit by the storm. She also asked other state officials to assess the extent of the damage caused by the cyclone.
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