The JKLF chief is also facing charges of kidnapping and murder for being allegedly involved in abducting Rubaiya Sayeed, daughter of then Union Home Minister Mufti Mohammad Sayeed.
The petitioner said that Yasin Malik was not able to even speak when his lawyer met him on April 20 in a hospital in Delhi.
The match, joined by PDP activists, started at the Town Hall and went up to the District Magistrate's office.
Additional Sessions Judge Rakesh Syal also sought a reply from the defence counsel on a plea of Tihar jail authorities seeking to produce Malik through video conference due to security concerns.
Malik, who was placed under arrest by the National Investigation Agency (NIA) in a case related to funding of separatists and terror organisations, had complained of chest pain on April 19.
Malik, who was shifted to Tihar jail under police protection, was taken into preventive custody in February by the Jammu and Kashmir police and shifted to Jammu's Kot Balwal jail.
Malik's sister on Saturday in a statement said that Malik was on hunger strike ever since the NIA shifted him to Delhi and following his deteriorating health was shifted to a hospital.
Addressing a press conference here, Malik's family said they were not allowed to meet the separatist leader and that he has been in a hospital for the past four days.
Malik will be facing questions from the NIA related to funding of his organisation.
Malik was on Tuesday shifted to Delhi's Tihar Jail after the NIA secured his production remand in connection with the terror funding case.
Malik was brought to the national capital Tuesday evening after a special NIA court in Jammu gave the go-ahead for his custodial interrogation by the probe agency.
Malik, who was arrested last month and shifted to Kot Balwal Jail in Jammu, will be facing questions related to funding of his organisation from the National Investigation Agency.
Banning the outfit under various provisions of the Unlawful Activities (Prevention) Act after a high-level meeting on security chaired by Prime Minister Narendra Modi.
The Centre's move comes after Islamabad invited separatist leaders to Pakistan's National Day event at the Pakistan High Commission in New Delhi on 23rd March, which India officially boycotted.
The authorities, meanwhile, enforced tough security restrictions in downtown Srinagar and parts of north and south Kashmir.