"We choose not to meet all party delegation and will send a joint memorandum to all. We have reiterated our four points for a peace process to begin. We propose talks between parliamentary committees of India and Pakistan," the moderate Hurriyat Conference chief said.
Mufti, on the other hand, said she would be sending a 15-member delegation for the interaction.
Jammu and Kashmir Liberation Front (JKLF) Yasin Malik along with hardline separatist leader Syed Ali Shah Geelani also refused to meet the 39-member all-party delegation..
The delegation includes senior parliamentary party leaders such as the BJP's Arun Jaitley and Sushma Swaraj, Samajwadi Party chief Mulayam Singh Yadav, CPI's Gurudas Dasgupta and JD (U) president Sharad Yadav.
The delegation, led by Home Minister P Chidambaram, is on a mission to restart the dialogue process with different sections of people in Jammu and Kashmir.
Meanwhile, Geelani and Mirwaiz Umar Farooq have been put under house arrest.