Mirwaiz, who is the chairman of moderate faction of Hurriyat Conference, and JKLF chief Malik were taken into custody at Abi Guzar after they, along with their supporters, took out a protest march from outside the JKLF head office there.
Several of their supporters were also taken into custody.
The separatists tried to move towards Lal Chowk city centre to stage a sit-in against the "harassment of people especially in south Kashmir" and "ill-treatment" of youth languishing in jails in the valley and outside.
"We ask the government to stop ill-treating our political prisoners, stop harassment of people in the name of militancy. They should stop crackdowns in south Kashmir where there is a military build up going on," Mirwaiz told reporters.
Alleging that the jailed youth were being treated like criminals which was against the Geneva conventions, he appealed human rights organisations and international community to impress upon India to repeal AFSPA and "other black laws".
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