The raids are being carried out in Chennai, Madurai, Tirunelveli and Ramanathapuram district, they said without divulging further details.
In the first case, the Delhi Police's Special Cell arrested one Syed Mohammed Zishan Ali, suspected to be linked to the terror outfit. He was arrested after being brought back from Saudi Arabia.
Asim Arun said he was living in the area for the past one month and earlier was residing in Deoband area of Saharanpur since 2011 and had also got his Aadhar card and passport prepared on fake identity.
Bangladesh on Sunday banned extremist Islamist group Ansar Al-Islam blamed for the brutal murders of several secular activists and atheist bloggers in the Muslim-majority country.
Bangladesh police sent the photos of the seven to Roy's widow Rafida Ahmed, who lost a finger during the attack.