The JKLF on Thursday called for strikes on Feb 9 and Feb 11 to observe the anniversary of Guru's execution, and then that of its founder Maqbool Bhat.
Shops and businesses were shut on Sunday, while there was little traffic on the roads in Srinagar and other parts of the occupied region.
Indian troops have erected iron barricades and laid concertina wire in parts of the region to block roads, with armed soldiers in full riot gear patrolling the streets to prevent any protests, a government official said.
He said low speed mobile internet, which was restored last month, had also been shut down as a precautionary measure.
Last month, India's Supreme Court rebuked the government for shutting down the internet and telecommunications in Occupied Jammu and Kashmir, which was India's only Muslim-majority state before it was split into two federally administered territories when New Delhi revoked its special status in August last year.
Indian security forces, meanwhile, have launched legal proceedings against JKLF for calling the strikes.
The JKLF was banned by India last year as part of a massive clampdown in Kashmir after an attack on Feb 14 in which 40 Indian troops were killed.
Its offices were closed and main leaders, including its chairman Yasin Malik, were detained. On Feb 9, 2013, Afzal Guru was hanged after the Supreme Court upheld a verdict that he was involved in a 2001 attack on parliament.
Maqbool Bhat was hanged in New Delhi's Tihar jail on Feb 11, 1984, following his conviction for the killing of a police official.
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