The National Tawheed Jamath is suspected of plotting the deadly Easter blasts.
Police said they have seized a large haul of explosives, a drone and a banner with the Islamic State logo.
Security has been beefed up in Sri Lanka as the army increased its deployment by 1,300 to 6,300.
The PM said the government knew that Sri Lankan nationals who joined the Islamic State had returned, but they could not be arrested as joining a foreign terrorist organisation is not against the law in the island nation.
'We believe that one of the suicide bombers studied in the UK and maybe later on did his post-graduate in Australia, before coming back to settle in Sri Lanka'
The names of both Maregowda and Puttaraju had figured in the list of missing Janata Dal-Secular workers tweeted by Chief Minister H D Kumaraswamy on Monday.
The input was sent through diplomatic channels to the island nation after a through investigation pertaining to the IS case in Coimbatore was carried out by the NIA.
-- Seven suicide bombers believed to be members of an Islamist extremist group carried out the series of explosions. -- Police have so far arrested 24 people - mostly members of an Islamist extremist group - in connection with the blasts
Forty suspects, including the driver of a van allegedly used by the suicide bombers, have been arrested in connection with the attacks which shook Sri Lanka.
National flags were lowered and people bowed their heads as the silence began at 8:30 am local time, the time the first of the attacks occurred on Sunday.