The group is said to be comprising of one Pakistani national and five Sri Lankans, the police said.
The police have beefed up security at places of worship, railway stations and other places where there is a large concentration of people.
"We have increased our security alert. All the vehicles are being checked thoroughly. About 200 police personnel are working round the clock," a senior police official in Nagapattinam district told .
He said a large number of policemen have been posted at the famed Velankanni Church in the district as a security measure.
According to him, security will be further beefed up at the Velankanni Church during the church festival from August 29 to September 8.
Similarly Hindu festival Vinayaka Chaturthi is going to be celebrated early next month.
The police in the coastal districts have also alerted the fishermen to keep a watch for any suspicious movement of boats at sea.
Meanwhile, intense checking by police continued in Coimbatore on Saturday as the six terrorists are suspected to be holed up in this textile town.
Coimbatore was rocked by serial bomb blasts in 1998 in which around 60 persons were killed. The police is carrying out checks at places of worship, railway stations, bus terminus, commercial establishments and other places.
( With inputs from IANS )