The agency said it had seized another vehicle allegedly belonging to the suicide bomber for examination. So far, it has interrogated 73 witnesses, including people injured in the blast.
The blast outside the historic fort was the first such explosion in the heavily guarded city since 2011.
Monday evening's attack took place at 18:52 local time (13:22 GMT) when a slow-moving vehicle stopped at a busy traffic signal and then exploded.
Within hours of the incident, Home Minister Shah confirmed the explosion had taken place in a white Hyundai i20.
Footage from the location showed remains of a charred white car and a number of other gutted vehicles, including an autorickshaw and cycle rickshaws.
Prime Minister Narendra Modi called the attack a "conspiracy", and his government vowed to bring the "perpetrators, their collaborators and their sponsors" to justice.
Opposition leader Rahul Gandhi said the news was "extremely heartbreaking".
Police on Thursday said they were investigating any links to the recent arrests of seven men by police in Indian-administered Kashmir.
Potential connections to the the recent seizure of 2,900kg of explosives from a Delhi suburb were also being probed, police said.
The Red Fort is visited by thousands of tourists every day, and was built in the 17th Century. Indian prime ministers use the Mughal fortress as a backdrop for their annual Independence Day speeches.
