Ceasefire was one of the important conditions in the peace deal and a HIA statement indicated that the group had started implementing the agreement.
'Butcher of Kabul' calls for peace as signs Afghan pact
"All mujahideen [fighters] of the Hizb-e-Islami are instructed to declare and respect a ceasefire after the signing of peace agreement between the organisation and the government," a statement said.
It added that both sides were bound to declare ceasefire under the agreement. "The government should also direct its security forces to stop attacks on HIA bases."
"The HIA has the right to defend itself if its people are attacked, unless a decision is taken about the armed groups," the statement said.
US may consider lifting sanctions on Afghan warlord
The deal paves way for Hekmatyar, who heads the now largely dormant militant group but has been in hiding for years, to make a potential political comeback despite a history of war crimes.
Hekmatyar was a prominent anti-Soviet commander in the 1980s who stands accused of killing thousands of people in the Afghan capital during the 1992-1996 civil war.
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