They also downplayed Basit's invitation to them for attending Pakistan's National Day celebrations.
Chairman of Hurriyat Conference Mirwaiz Umar Farooq, who met Basit yesterday, said the "complex" Kashmir issue needed a "political approach".
"Hurriyat's main agenda is that stakeholders involved -- India, Pakistan and Kashmiris -- will have to move together to solve the problem.... It is the only way out to avoid killing of innocent civilians and army men and other destruction.
Echoing similar sentiments, Jammu and Kashmir Liberation Front (JKLF) Chief Yasin Malik said he has been attending the Pakistan National Day celebrations over the past 22 years.
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"I am here just to attend the function as so many other people here will be... Indian politicians, Indian journalists will be there. It's a function I am attending for the last 22 years," he said.
India had called off foreign secretary-level talks with Pakistan last year after Basit held consultations with Hurriyat leaders on the eve of the official talks.
This meeting comes a fortnight after Basit had gone to the Delhi residence of hardline Hurriyat leader Syed Ali Shah Geelani and updated him about the visit of Indian Foreign Secretary S Jaishankar to Islamabad and issues discussed during his meetings there.
While meetings between Pakistani diplomats and Kashmiri separatist Hurriyat leaders have been a regular practice for the last 30 years, the issue has always irked India, which has maintained that resolution of Indo-Pak issues including Jammu and Kashmir have to be done bilaterally between the leadership of the two countries.