Thailand declared on Sunday a tsunami alert but cancelled it less than 90 minutes later, while Indian officials said there was no danger of a huge wave like the one that hit in December.
"There is no tsunami warning from the Indian side," Indian Science and Technology Ministry spokesman Sitanshu Kar told Reuters in New Delhi.
"The government is asking people to remain calm. The essential precondition for a tsunami is that the earthquake should be of 7.5 magnitude and this is below it."
Sunday's earthquake came seven months after the 26 December tsunami, triggered by a 9.15 magnitude earthquake. About 227,000 are dead or missing after the tsunami.
India's Science and Technology Minister Kapil Sibal also dismissed talk of a tsunami.
"Any talk of a tsunami as of now should not be taken heed of," Sibal told Indian television channels. "It has been two hours since the earthquake. If the tsunami was coming, it would have come by now."
The quake hit the area off India's eastern coast at 1542 GMT measuring 7.0, according to the US Geological Survey (USGS) which initially urged authorities near its epicentre to be aware of the risk of local tsunamis.