The first delegation was led by former chairman of moderate faction of Hurriyat Conference Abdul Gani Bhat which was followed by a team of hardline Hurriyat led by Syed Ali Shah Geelani.
After his hour-long meeting, Bhat told PTI that it is important for peace in India and Pakistan that there should be friendship between the two countries.
"We are with any such move that forges a new era of friendship between two neighbours of the South Asia. We have to understand that dialogue is the only way to move forward," he said.
"He (Basit) told us that both the countries were moving towards resolution of all outstanding issues including Kashmir," Bhat said, adding "he sought help from Hurriyat Conference in contributing towards building an environment for that."
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He regretted controversies created over the meetings between separatists and the Pakistani High Commissioner saying "I wonder why are some people seeing red. I pray that they should get the sense of urgency of having a good relations between the neighbouring countries."
Hurriyat Conference Chairman Mirwaiz Umer Farooq, who held a separate one-to-one meeting with Basit on Sunday, also said that speculation in media should not be given importance.
"The matter is whether there ia political will between the two countries to go together. Media cannot make the government hostage, it cannot make the situation of Kashmir or Kashmir policy as a hostage," the Mirwaiz said.