There have been scenes of panic in coastal areas of southern India and the Andaman islands after the government warned of new wave dangers.
Tamil Nadu bore the brunt of Sunday's tsunami in India
They said aftershocks near the Andaman and Nicobar islands could cause more devastating high waves.
Thousands of people fled inland from the coast of Tamil Nadu, where more than 6,000 deaths have been confirmed.
Separately, Indian premier, Manmohan Singh, has been visiting disaster-hit areas in southern states.
There have been a series of aftershocks around the Andamans since Sunday's massive undersea earthquake. None have triggered large waves.
Indian Home Minister Shivraj Patil sought to alleviate fears when he spoke to journalists in Delhi later on Thursday.
"Let us not create panic, panic is different from precaution," he said. "We should take precaution."
Mr Patil said the government had received "some information" that an earthquake may occur.
"If the earthquake measured above seven on the Richter scale, a tsunami may occur, may occur," he said.
In its initial warning, Mr Patil's home ministry asked state governments to be on alert and maintain a vigil on the sea.
The government in Tamil Nadu advised people to retreat 2km (1.2 miles) inland.
The BBC's Charles Haviland says there was total panic in the port of Nagappattinam, one of the areas worst hit by Sunday's waves.
"Vehicles travelling into Nagappattinam from the south were met by a surge of traffic coming the other way," he says.
"Cars, buses, trucks, pedestrians and cyclists were all fleeing inland."
Our correspondent says it seems the federal government is being ultra-cautious after being accused of being caught unaware by Sunday's disaster.
The result is that many people have fled their homes right along the coast of Tamil Nadu, including in its major city, Madras (Chennai).
In the Andaman and Nicobar islands in the Indian Ocean, much closer to the epicentre of the quake, the warning was much more stark.
The region's senior official, Lieutenant Governor Professor Ram Kapashe, told journalists he had scientific information that a tsunami could strike the island sometime in the afternoon.
He was speaking in the main town in the Andamans, Port Blair.
His warning led hundreds of people to rush out of their homes and offices in panic.
The BBC's Geeta Pandey in Port Blair says at least 10,000 people are believed to be dead or missing in the Andaman and Nicobar islands.
Prime Minister Manmohan Singh on Thursday visited relief camps and hospitals in Kanyakumari in Tamil Nadu and in Trivandrum in neighbouring Kerala.
Mr Singh said: "The government will assure you that rehabilitation work will be carried out well. Steps will be taken to ensure all affected people have means to live with self-respect."