A total of 147 people, 132 of them children, were killed when Tehreek-i-Taliban Pakistan militants stormed Army Public School in Peshawar in 2014.
The agreement was reached amid ongoing peace talks between the government and the TTP that began last month. Chaudry said the truce could be extended if talks continue to make progress.
Four terrorists associated with the banned Tehrik-e-Taliban Pakistan were killed on Tuesday in a police operation in northwest Pakistan.
The TTP, commonly known as the Pakistani Taliban, is a banned terrorist organisation based along the Afghan-Pakistan border.
Pakistan has been claiming that India was behind some of the terror attacks in the country recently.
The Dawn newspaper reported that one of the country's major concerns has been the presence of the banned Tehreek-e-Taliban Pakistan (TTP) terrorist group in Afghanistan.
Commander Safiullah was involved in planning and execution of improvised explosive device attacks on security forces, extortion and kidnapping for ransom, army said.
The Frontier Corps South soldiers were attacked in the mountainous Buleda area of Kech district on Friday.
Technical issues still remain for formation of new Afghanistan government, want to join CPEC project: Taliban
The latest statement comes amid the conflicting reports of Panjshir, the last Afghan province to fall under the control of the Taliban as National Resistance Forces (NRF) have rejected the claims.
Militants from the TTP or Pakistani Taliban have carried out major terror attacks across Pakistan in recent years.
The 28th report of the UN Analytical Support and Sanctions Monitoring Team says that terrorists from a variety of countries and militant groups continue to operate in Afghanistan.
The Trump administration today asserted that it firmly supports the territorial integrity of Pakistan and does not support Baloch insurgency or any group that threatens the country.