The Hurriyat leaders are the real representatives of the Kashmiri people and India will have to accede to this fact, the foreign office spokesman said.
This is the first result of talks between the PM and Hurriyat.
They will be here on an invitation of SAFMA's Indian Chapter.
Mirwaiz will be in New York for the Organisation of Islamic Conference general council meeting and Musharraf would be there to attend the United Nations General Assembly meeting.
Geelani, who Islamabad's backing, is understood to have impressed upon Kasuri to do more on involving Kashmiris in the dialogue process.
The separatist leader was scheduled to attend the funeral prayers of militant commander Manzoor-ul-Islam, who was killed in an encounter with security forces on Wednesday night, his spokesman said.
Union Home Minister Shivraj Patil had said yesterday that the talks would be held 'within the four walls fo the Constitution'.
"What is the point of holding discussion with the government to government level by New Delhi?" askeed the Mirwaiz.
Vohra, whose efforts had resulted in two rounds of talks between the All Parties Hurriyat Conference and former deputy prime minister L K Advani, quit the post citing that his appointment had been made by the previous government
"We have no objection if they [the Hurriyat leaders] want to travel to Delhi and hold talks with the Indian leadership," he said.
He is suspected to be suffering from cancer in the kidney.
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.
'These militants are our relatives, our brothers. How can we watch the security forces kill them?' Political Front leader Mohammed Musadiq Aadil explains why they pulled out of the dialogue with the Centre.
'I have dissolved the executive committee of the Peoples Conference and expelled Sajjad from the party,' Bilal said in Srinagar.
A joint committee set up by Jammu and Kashmir and the central government recommended the revocation.
Chief Minister Mufti Mohammed Sayeed said the release of the detainees had nothing to do with the talks between the All Parties Hurriyat Conference and Deputy Prime Minister Lal Kishenchand Advani on Thursday in New Delhi.
This is the first meeting between the Hurriyat and an Indian prime minister.