NIA officials questioned Bilal Malik, Panna Ismail and Police Fakrudeen housed in the Central Jail in Puzhal, here.
The questioning follows the recent raids in Coimbatore and Madurai in Tamil Nadu and the arrest of persons who are sympathisers of proscribed Islamic State (IS).
THe NIA move came as the Coimbatore police arrested three alleged IS sympathisers planning terror attack.
On June 12, the NIA had conducted searches at seven locations in Coimbatore and seized incriminating material, including books and documents, from the houses and work places of six accused persons.
The anti-terror agency registered a case on May 30 against the six, who were allegedly propagating ideology of the IS/Daesh on social media with the intention of recruiting vulnerable youth into the organisation for carrying out terrorist attacks in south India, especially in Kerala and Tamil Nadu.
The NIA said some of the accused and their associates were in touch with Zahran Hashim, the mastermind of the Easter Day bombings in Sri Lanka that killed around 250 people, and his associates over social media, with the intention of furthering the objectives of the IS in India.
The NIA questioned the accused about the incriminating material recovered during searches, the content of their social media accounts and on the basis of information provided by pro-IS Shiek Hidayathullah Y. who was arrested on June 14.
Scrutiny of documents seized from Hidayathullah's house revealed that he was associated with proscribed terrorist organization, the Student Islamic Movement of India (SIMI) as well.
On June 12, the NIA had arrested Mohammed Azarudeen, a social media friend of Hashim.
( With inputs from IANS )