Malik, who is in jail following his conviction and life sentence in a terror funding case, was brought to the high-security apex court premises in a prison van escorted by armed security personnel without the court's permission.
Singh's meeting with Malik comes a week ahead of his talks with a cross-section of political parties and separatists groups from the state.
They were protesting against alleged human rights violations in Kashmir.
Turning down the court's suggestion to appoint a lawyer on his behalf, separatist leader Yasin Malik on Friday told the Delhi high court he wished to argue in-person against a National Investigation Agency plea seeking death penalty for him in a terror funding case.
'I am worried that Pakistan will still feel compelled to take substantive military action beyond this apparent drone activity.' 'If so, the crisis could persist for a while more and dangerous days are still ahead.'
Malik again insisted on his physical appearance in the hearing on the killing of four Indian Air Force personnel in 1990.
Mushtaq Ahmed Zargar, who was involved in a series of terror attacks in Jammu and Kashmir and was one of the released terrorists in the hijacking of Indian Airlines flight IC-814 in 1999, has been designated as a terrorist by the Union government.
'It is typical of China's strategic deception of making virtue out of necessity,' observes Rup Narayan Das.
London-based Jammu and Kashmir Liberation Front pans other separatists who gave the Kashmir roundtable a miss.
Human Rights Forum chairman Mohammad Ahsan Untoo and Jammu Kashmir Liberation Front Vice-Chairman Javed Ahmed Mir were trying to take out a procession against the death sentence given to three persons in the Parliament attack case.
Two policemen were injured when Jammu and Kashmir Liberation Front supporters clashed with security men in Lal Chowk area of the city after Friday prayers demanding handing over of mortal remains of JKLF founder Mohammad Maqbool Bhat.
Dulat, who was advisor on Jammu and Kashmir to the central government during the tenure of former prime minister Atal Behari Vajpayee, also advocated the need for starting a dialogue with Pakistan.
The Jammu and Kashmir Liberation Front chief, 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 has submitted a letter to the doctors at the medical facility, saying he did not want to be treated.
Ali Mohammad Mir, who is the prime accused in the kidnapping case after Malik, had taken Rubaiya Sayeed in his vehicle to Sopore from Srinagar and kept her at a guesthouse.
A special court in Jammu on Tuesday issued a bailable warrant against Rubaiya Sayeed, the daughter of former Jammu and Kashmir chief minister Mufti Mohammad Sayeed, after she did not appear for cross-examination in a case related to her abduction by the JKLF in 1989.
This has also raised concerns over undetected infiltrations from across the Line of Control and terrorists potentially residing in the outskirts of cities and villages, they said.
'There is a trust deficit between Delhi and Srinagar. It is there even today.'
He said that even the security of the Supreme Court would have been put to a serious risk if any untoward incident were to happen.
'The so-called separatists are representatives of Pakistan. They get paid from Islamabad for propagating that country's policy and conniving in her ploy of accession of Kashmir to Pakistan.'
Among the national parties, the Congress, Aam Aadmi Party, the Bahujan Samaj Party and the Communist Party of India-Marxist opposed the proposal, while the Bharatiya Janata Party and the National People's Party supported it.
Liberal Democrat Member of the European Parliament Chris Davies said the decision showed the Indian government was trying to hide the "reality of its actions" and blocking absolute freedom of the press.
Protests rocked parts of Kashmir Valley including Srinagar on Saturday where Pakistan and Islamic State flags were yet again displayed by masked youths after Eid prayers.
Restrictions were imposed in north Kashmir and some areas of central Kashmir to thwart the march announced by separatists to Jamia Masjid.
Authorities clamped strict restrictions in Srinagar and north Kashmir's Sopore town to foil a separatist march on Friday.
"We intend to talk to individuals and groups who want peace and normalcy in Kashmir Valley," Home Minister Rajnath Singh said before the departure of delegation comprising 30 members from 20 parties.
Curfew-like-restrictions were imposed in the old city of Srinagar and some uptown areas to foil protests and a sit-in at the historic Jamia mosque after the Friday prayers.
Congress MP Shashi Tharoor said Afzal Guru's hanging was both "wrong and badly handled".
Groups of youth took to the streets at Press Colony and Khanyar in support of Naik.
The National Investigation Agency has charge sheeted Dilawar Iqbal -- a right-hand man of Jaish-e-Mohammed (JeM) chief Maulana Masood Azhar Alvi -- and Kupwara-resident Mohammed Ubaid Malik for allegedly conspiring to disturb the peace and communal harmony of Jammu and Kashmir by attacking security forces, officials said on Wednesday.
Harsh Vardhan Shringla said New Delhi's move to abrogate Jammu and Kashmir's special status last month and bifurcate it into Union territories was done for the 'benefit' of the people.
Separatists dismiss breakthrough in dialogue between the neighbours in Russia, says talks shouldn't be for time pass
The depiction of hijackers of the Indian Airlines flight from Kathmandu to Delhi has kicked off a row with a section of viewers objecting to the 'humane' projection of the perpetrators.
The detentions come ahead of a crucial hearing on Article 35-A in Supreme Court which is likely to take place on Monday. The article, incorporated into the Indian Constitution in 1954, grants special rights and privileges to the citizens of Jammu and Kashmir.
Curfew remained in force on Thursday in parts of Kashmir valley as a preventive measure to maintain law and order after a youth was killed when security forces allegedly opened fire to chase away stone-pelting protesters.
'How you live serves as a much better track record than your timeline,' says Mitali Saran.
Malik began an indefinite hunger strike on July 22 after the Centre did not respond to his plea that he be allowed to physically appear in a Jammu court hearing the Rubaiya Sayeed abduction case in which he is an accused.
The former IAS officer said the main reason for not contesting the polls was to focus more on the mass contact programme.
Clashes between protesters and law enforcing agencies were reported from Sopore, Anantnag, Rajpora, Shopian towns and Safakadal area of the city.