In a surprise move on Wednesday, Hurriyat chairman Moulavi Abbas Ansari quit and handed over charge to the Mirwaiz.
The meeting comes ahead of Dr Singh's meeting with Musharraf to be held on the sidelines of the UN General Assembly.
Facilitating the return of expatriate Kashmiri leaders will also feature in the first meeting between the Centre and All Parties Hurriyat Conference.
'India should be more confident and let Pakistanis meet Hurriyat leaders. India's main concern is terrorism, and India should talk terrorism. If that means talking Kashmir, so be it. India can't answer terror with terror because we don't have terror factories. India can't answer terrorism with war because we both have nuclear weapons. That leaves talks as the only option,' says Shivam Vij.
Hurriyat said Dulat's "primary goal was to defame the Kashmir freedom movement and spread lies about it".
After the cancellation of National Security Advisor-level talks, proposed meetings between top military officials of India and Pakistan are now unlikely, a media report said on Monday.
After the meeting with the Pak PM, separatist leaders admitted that differences persisted.
India and Pakistan have no right to impose leaders or solutions on Kashmiris who have sacrificed their lives and honour for a sacred cause, he said.
The meeting presided over by APHC chairman Moulvi Mohammad Abbas Ansari is being attended by all senior members, including executive members Mirwaiz Umer Farooq, Abdul Gani Bhat and Bilal Gani Lone, Hurriyat sources said.
Separatist Kashmiri leader Ghulam Nabi Fai, who has been arrested by the Federal Bureau of Investigation on charges of working for Pakistan's Inter-Services Intelligence, was the point man of contact for the Hurriyat leaders whenever they visited the United States.
Breaking the ice, the Centre's interlocutors on Kashmir talked to Hurriyat Conference chairman Mirwaiz Umer Farooq over the phone discussing the situation in the state and seeking time for a meeting.
Dr Sameer Kaul, Hurriyat leader Syed Ali Shah Geelani's personal physician, speaks about Kashmir's hardline separatist.
'As far as I know Burhan Wani did not kill anyone.'
In a significant move, separatists have decided to hold talks with Kashmiri Pandit migrants to discuss their return to the Valley.
Hurriyat's Mirwaiz said Mufti has exposed his game plan by rushing to New Delhi to sort out the matter.
Both factions of Hurriyat Conference on Tuesday attacked Jammu and Kashmir Chief Minister Omar Abdullah in unison over his statement asking to explore "other options" if Pakistan continues with ceasefire volition, saying his talk of "bullet for bullet" shows lack of understanding of the consequences.
Top Kashmiri separatist leaders on Saturday evening joined the iftar party hosted by Syed Ali Shah Geelani, the hard-line separatist leader at his uptown residence.
The All Parties Hurriyat Conference on Wednesday announced the resumption of protests by calling a general strike on Saturday.The APHC co-ordination committee decided to call the strike after holding a meeting in Srinagar today afternoon to decide its future course of action."The coordination committee has appealed to the people to hold peaceful protests after Friday prayers and observe a complete strike on Saturday," a spokesman of the committee said.
Major opposition political parties and separatists groups in J&K on Wednesday slammed the move of the government to create separate townships for Kashmiri pandit migrants.
Addressing the congregation at the historic Jamia Masjid in old city Srinagar on Friday afternoon, the Mirwaiz said: "We will oppose all efforts aimed at fanning division of the Kashmiri Muslims on sectarian lines. If need be, we will expose the elements and institutions patronised by the government for the purpose."
India on Monday said there was 'no scope for misunderstanding or misrepresenting' its position
Pakistan's ruler Pervez Musharraf and his top diplomats made a U-turn on talks with India after the then Prime Minister Atal Bihari Vajpayee released Hurriyat leaders in early 2000 as part of his peace initiatives on Kashmir, according to a declassified US cable.
Geelani, who was a member of banned Jamaat-e-Islami and chairman of hardline Hurriyat Conference, had been suffering from various ailments for nearly last two decades.
Jilani said Pakistan had not received any "official communication" from the Indian side in this context and described the visit of the Hurriyat delegation as "a positive development".\n\n
Chairman of All Parties Hurriyat Conference Syed Ali Shah Geelani on Saturday condemned the hanging of Afzal Guru, saying the latter was not involved in the 2001 Parliament attack and was also not given a chance to defend himself in connection with this case. Geelani said Guru's hanging at the Tihar Jail this morning is a matter of sorrow and pain for the people of Jammu and Kashmir.
"It (JeI's statement) is a very valid thing. Islam seeks such a society where human values are respected, where modesty is upheld, where semi-naked dresses are not worn, where alcohol and drugs are not promoted and where women and men do not mix," Geelani said.
"We can't have this high-horse spirit -- that you can speak to the high commissioner of Pakistan, but not to the home minister of India."
Unfazed by India's strong reservations, Pakistan said it will go ahead with its engagement with Kashmiri separatist leaders when National Security Advisor Sartaj Aziz goes to New Delhi for talks with his Indian counterpart Ajit Doval on Sunday.
Hurriyat Conference leaders Mirwaiz Umar Farooq and Bilal Lone were on Thursday manhandled allegedly by a group of Kashmiri Pandit activists who stormed a seminar being attended by them in Chandigarh.
India on Friday made it clear to Pakistan that it should not go ahead with the meeting of its NSA Sartaz Aziz with Hurriyat representatives in New Delhi when he comes to hold talks with his Indian counterpart Ajit Doval, saying it will not be "appropriate".
The National Investigation Agency (NIA) on Monday attached 17 properties of Kashmiri businessman Zahoor Ahmed Shah Watali in a terror funding case, the agency said.
Pakistan on Friday claimed that any talks between the Indian government and separatist Kashmiri leaders will not be successful without its involvement.
"Whether we are back or away, if they put Kashmiri Pandits in isolation, they will never see peace in Kashmir."
Kashmiri separatist groups on Sunday met Pakistan Prime Minister Nawaz Sharif's advisor Sartaj Aziz here, drawing a sharp reaction from Bharatiya Janata Party which said the government is committing a "diplomatic blunder" by allowing this.