The reduction of violence will include a halt in conducting suicide attacks in major cities, and the group will also not block major highways, TOLO News reported citing the sources as saying on Thursday.
"The Taliban said that they will not agree on a ceasefire; however, a partial agreement was reached about the reduction of violence and the final decision regarding the issue will be announced by the Taliban's leader," said Mawlana Jalaluddin Shinwari, a former group member.
"A reduction of violence would mean a halt to major attacks, and the Taliban will not try to take over districts and will avoid blocking major highways," said another former member.
The Afghan government has insisted on a reduction of violence and a ceasefire as preconditions for talking to the Taliban.
The US and the Taliban representatives will soon meet, the sources added.
Marathon talks initiated between the US and the Taliban in October 2018 in Doha to find a negotiated settlement for Afghanistan's lingering crisis broke down in September following a Taliban-linked car bomb that killed 10 people including an American soldier in Kabul.
The talks resumed on December 7 but was again suspended in the wake of a deadly truck bomb that targeted the main US military base in Bagram on December 11, which left eight dead including six attackers and injured over 70 civil.
( With inputs from IANS )