Besides Geelani's son-in-law Altaf Ahmed Shah, popularly known as Altaf Fantoosh, the court sent Peer Saifullah, Mehrajuddin Kalwal and Nayeem Khan to the agency's custody.
The NIA sought 12 days of custody, saying they were required to be confronted with each other and with the evidences gathered in the case.
The agency had arrested seven persons on July 24 in the case of alleged funding of terror and subversive activities in the Kashmir Valley to fuel unrest.
Senior advocate Siddhartha Luthra, appearing for the probe agency, said that Fantoosh and three others were required to be taken to distant places in the Valley in connection with the probe.
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A lawyer associated with the case said that during an in-chamber proceedings, the NIA also requested the court to put its remand application in a sealed cover as it contained various sensitive informations, which was allowed by the court till next date of hearing.
The money was being raised to fund separatist and terror activities in restive Jammu and Kashmir, it had said, alleging that the accused were waging war against the country and they were involved in various offences punishable under Unlawful Activities (Prevention) Act.
It added that the accused were involved in creating unrest by way of anti-India demonstrations and bandhs, which were done on their and others' instructions.
Shah was in the custody of Jammu and Kashmir Police, which had put him under preventive detention immediately after Eid last month.
Geelani's close aides Tehreek-e-Hurriyat spokesman Ayaz Akbar and Peer Saifullah were arrested by the NIA from the valley.
Shahid-ul-Islam is the spokesman of the moderate Hurriyat Conference led by Mirwaiz Umer Farooq.
Hafeez Saeed, the Pakistan-based chief of the JuD, the front of the banned Lashkar-e-Taiba (LeT), has been named in the FIR as an accused, besides organisations such as the Hurriyat Conference, Hizbul Mujahideen (HM) and Dukhtaran-e- Milat.
The raids were part of the NIA's efforts at clamping down on separatist groups allegedly receiving funds for subversive activities in the valley.
The NIA had claimed that it recovered account books, Rs 2 crore in cash and letterheads of banned terror groups, including of the LeT and the HM, during the raids.