He was quoted by the BBC as saying that the process should continue.
This is the first meeting between the Hurriyat and an Indian prime minister.
The moderate faction of Hurriyat Conference on Wednesday asked people to cancel the reception arranged for its seven-member delegation returning from Pakistan on Thursday.
The decision is a 'small yet significant step' towards the final settlement of the Kashmir issue, Hurriyat leader Abdul Gani Bhat said.
The people of Jammu and Kashmir had high expectations from the Prime Minister's visit with regard to the political resolution of the Kashmir issue."
"We have followed the proper method in applying for passports, but it seems the government is not interested in allowing the visit."
Before leaving for a conference of Asian NGOs to be held in Hyderabad, Hurriyat leader Mirwaiz Umer Farooq said that during the meet he would highlight the need for tripartite talks on the issue.
Chairman of the moderate, All Parties Hurriyat Conference Mirwaiz Moulvi Umar Farooq on Friday lambasted the government for 'wooing tourists from Israel'.
Facilitating the return of expatriate Kashmiri leaders will also feature in the first meeting between the Centre and All Parties Hurriyat Conference.
Mirwaiz Farooq, who is also a Muslim religious head, feels that the Friday meeting of Prime Minister Narendra Modi with his Pakistani counterpart Nawaz Sharif in Lahore has given a fresh hope not only to people of the two nations but to the entire South Asian region.
After the meeting with the Pak PM, separatist leaders admitted that differences persisted.
Ahead of its Pakistan visit from Monday, separatist outfit Hurriyat Conference Sunday said it will discuss the Kashmir issue with President Pervez Musharraf and other Pakistan leaders.
The Hurriyat says on the one hand India and Pakistan should talk to each other and on the other the Hurriyat leadership would have separate dialogue with India and Pakistan.
'We know the resolution of the Kashmir issue can only be found through dialogue. We are not shying away from that,' Mirwaiz Omar Farooq said.
Terming the ongoing polls in the state as a "drama", moderate faction of Hurriyat Conference headed by Mirwaiz Umer Farooq on Monday appealed to the international community to send delegations to Jammu and Kashmir on a fact-finding mission.
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.
Several leaders of moderate Hurriyat Conference, including its chairman Mirwaiz Umar Farooq, were placed under house arrest by the authorities in Srinagar after the separatist amalgam said it will visit the family of Parliament attack convict Mohammad Afzal Guru.
Reacting to National Conference patron Farooq Abdullah's appeal to separatists to come forward for talks to solve the Kashmir issue, the moderate faction of Hurriyat Conference on Monday termed the suggestion as one born out of "frustration".
Three Hurriyat Conference leaders were taken into custody, as police foiled the separatists plan to march in connection with Martyrs day on Monday.
A senior Hurriyat leader has created a flutter by saying that two separatist leaders and his brother were killed by "our own people" and not security agencies, prompting Jammu and Kashmir government to term it as a "late admission" and a call for a probe to fix responsibility.
Mirwaiz to lead Hurriyat delegation to PoK
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.
The announcement came a day after Hurriyat chairman Maulvi Abbas Ansari expressed willingness to hold the talks if the Centre extended an invitation.
Extremists groups have warned the Hurriyat Conference not to hold talks without first consulting them.
Interestingly, the Hurriyat leaders had earlier agreed to meet Dr Singh on either of the two dates proposed by his office. What made them suddenly change their mind is not known.
Mohammad Rafiq Shah was president of the J&K Peoples Liberation League.
The moderate Hurriyat Conference on Wednesday condemned the killing of two sisters at Sopore in Jammu and Kashmir's Baramulla district terming it as an inhuman act. The statement hit back at those who had questioned separatists' silence over the killings.