54 people have been killed in neighboring Andhra Pradesh and two in Puducherry.
Tamil Nadu Chief Minister J. Jayalalithaa urged Prime Minister Narendra Modi to declare the unprecedented crisis a national disaster.
Modi flew into Chennai and announced Rs.1,000 crore - Jayalalithaa had sought Rs.5,000 crore - in immediate relief after an aerial survey of some of the worst hit areas. "We are all pained by the devastation," Modi said. In New Delhi, Home Minister Rajnath Singh said the situation in Chennai and three other districts was "alarming".
"It indeed is alarming," Chennai-based lawyer Elangovan told IANS, adding that thousands of people were fleeing the city that has been virtually cut off after highways and railway tracks came under water and the airport was ordered shut till Dec. 6.
"The situation in Tamil Nadu is alarming. It is not an exaggeration to say that Chennai has turned into an island," Rajnath Singh said.
Chennai suffered unprecedented destruction, with water overflowing from rivers and reservoirs seeping into scores of apartments and houses, markets, shopping malls, offices and educational institutions, unsettling life like never before.
Though there was respite from the rains and the army, navy and air force and the National Disaster Response Force worked hard to rescue the marooned and provide relief, the water level did not show major signs of receding.
Residents complained about lack of medicines, milk, potable water, vegetables and public transport. More than 164,000 people were housed in 460 camps in Chennai, Cuddalore, Thiruvallur and Kanchipuram districts. Many thousands also shifted to others' houses after water entered theirs.
In several places, power supply and communication lines were down, adding to the misery.
"I have had no drinking water and milk since yesterday," Harish Rao told IANS from his house in south Chennai.
The worst hit were the poor, tens of thousands of who live in shanties in low-lying areas. Hundreds were stranded at the railway stations. Banks advised customers to use ATMs to take out cash as some branches would not open.
Surinder Singh, a doctor from Delhi who was stuck in Chennai, told IANS: "It looks like the entire city is under one foot of water. In some places, the water level is more. Flood water has reached almost every locality, including posh areas. Everyone on the streets is barefoot."
Jayalalithaa, who had a meeting with Modi, said over 4.2 million food packets were provided to people and those living in apartments in affected areas were given water bottles and food by helicopters and boats.
She said the power supply would be restored once the water was drained out of the flooded areas.
The railways cancelled 20 trains out of Chennai Central and Chennai Egmore stations and seven trains from other stations.
People in many areas opened up their homes to the distressed. Some gave away food to those marooned. Hundreds had moved to rooftops in the hope of getting food packets from military helicopters.
The Modi government has agreed to deploy 10 additional army columns and 20 NDRF teams in the state.
Chennai has been battling heavy rains since early November due to a low pressure area over southwest Bay of Bengal.