These 14 accused were brought in a special aircraft to Chennai where they were produced before Special Judge Senthur Pandian of NIA court in Poonamallee, they said.
After hearing the NIA's arguments, the court remanded all the accused to agency's custody till July 25, they said.
It is alleged that these people have been collecting money to set-up terror outfit 'Asnarulla' in Tamil Nadu and are believed to have been deported from Saudi Arabia recently, they said.
The NIA had said it arrested two persons -- Hassan Ali and Harish Mohammed -- in the case on Saturday.
The agency had said it has busted a gang which allegedly conspired, collected funds and made preparations to carry out terrorist attacks in India with the intention of establishing Islamic rule in the country.
It had also held searches in the premises belonging to the three accused located here and at Nagappattinam district in connection with the case.
According to credible information, the accused men, while being within and beyond India, had conspired and conducted consequent preparations to wage war against the Government of India by forming the "terrorist gang Ansarulla", the NIA had said in a release.
A case was registered on July 9, 2019, (Tamil Nadu Ansarulla Case) against Syed Bukhari, a resident of Chennai, and Hassan Ali Yunusmaricar, and Mohammed Yusuffudeen Harish Mohamed, both natives of Nagappattinam, and others, it said.
Various sections of the Indian Penal Code, including criminal conspiracy, waging or attempting to wage war against India, and terror charges under the Unlawful Activities (Prevention) Act has been slapped against them.
During the searches, nine mobile phones, 15 SIM cards, 7 memory cards, 3 laptops, 5 hard discs, 6 pen drives, 2 tablets and 3 CDs/ DVDs besides documents, including magazines, banners, notices, posters and books were seized by the NIA.