In the first instance, Mirwaiz, the chairman of moderate Hurriyat Conference, came out from his Nigeen residence located on the outskirts of Srinagar this afternoon.
He was immediately detained by the police and taken to Nigeen police station, officials said.
Separately, Geelani, who heads hardline faction of Hurriyat Conference, also tried to take out a march from his Hyderpora residence on Srinagar-Airport road.
However, the police stopped the octogenarian leader, following which he along with his supporters staged a sit-in on the link road, officials said.
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The two Hurriyat factions as also JKLF led by Yasin Malik had given a call for 'Lal Chowk March' today and tomorrow to press for 'right of self-determination' in accordance with the UN resolutions.
While Mirwaiz and Geelani have been under house arrest, Malik is lodged in central jail here since his arrest on July 9 following widespread clashes in the aftermath of the killing of Hizbul Mujahideen commander Burhan Wani.
Prior to his arrest, Mirwaiz accused the central government of trying to hoodwink the people of the country and international community "by keeping a lid on the ground realities" in the valley.
He said "the reality is that the people of Kashmir neither demand employment or contracts nor the subsidy. The only demand of the people is freedom and restoration of their rights. So the Indian government should read the writing on the wall."
Apparently referring to India's stand that the ongoing unrest in the valley is sponsored by Pakistan, Mirwaiz said, "repeatedly attempts are being made that the ongoing movement in Kashmir is sponsored and somebody is pushing it from behind.
"Our programme and our stand is crystal clear - the right of self-determination is the basis of our struggle," he said.
He said no election, no economic package and "so-called" political initiative would work in Kashmir till the issue is resolved in accordance with the UN resolutions.
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