Additional Sessions Judge Sidharth Sharma extended the custody of Shah and Mohammad Aslam Wani till September 27 when they were produced before the court through video-conferencing after expiry of their earlier custody.
During the arguments, Shah's advocate M S Khan told the court his client was not given proper medical and other necessary facilities in the jail. The court has sought a reply from the authorities concerned on Khan's submission.
Shah was arrested by the Enforcement Directorate on July 26, a day after several Hurriyat leaders were taken into custody of the National Investigating Agency (NIA) in a case of alleged terror funding in the Valley.
The agency had earlier issued summonses to Shah in the case, the prosecution had said, adding that Wani had claimed that he had given Rs 2.25 crore to the separatist leader.
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Wani, 35, was arrested in the latest case on August 6 by the ED after a sessions court here had issued an open-ended non-bailable warrant (NBW) against him.
According to an ED official, Wani was arrested in Srinagar with the help of the state police and later brought to Delhi.
The ED had issued multiple summonses for his appearance in the case, but he did not present himself before it.
The ED had registered a criminal case under the Prevention of Money Laundering Act (PMLA) against Shah and Wani.
Investigating agencies such as the NIA have cracked down on Hurriyat leaders, arresting Syed Ali Shah Geelani's son- in-law -- Altaf Ahmed Shah, also known as Altaf Fantoosh -- and six other Kashmiri separatists in alleged terror funding case.