A Taliban spokesman has told Afghan media that the peace deal with the US is finalised and will be signed by the end of February.
The agreement would be the prelude to ending America's longest war.
The US invaded Afghanistan in 2001 to topple the Taliban government, saying it allowed Al Qaeda to use the country as a base to plan and execute the September 11 attacks that killed 2,977 people and wounded more than 6,000.
After nearly 20 years of fighting, the US began secret talks with the Taliban in July 2018, leading to rounds of dialogue led by its special representative for Afghanistan reconciliation, Zalmay Khalilzad.
The process has stopped and started several times, stumbling over key issues such as a roadmap to withdrawing US and Nato troops from the country and the start of direct talks between Kabul and the Taliban.
The insurgents have refused direct talks with the Afghan government, which they say is illegitimate.
But Kabul has tried to build consensus on talks, holding large tribal legal assemblies called the loya jirga.
US President Donald Trump has repeatedly said he wants to bring home US troops from Afghanistan. It was an often repeated line in his campaign speeches before the 2016 election.
At the Munich Security Conference last weekend, Afghan President Ashraf Ghani told a panel that his government was taking a practical approach to resolving the 18-year Afghan conflict.
"We are not going to solve this conflict on the basis of 'paper discussions'," Mr Ghani said.
He expressed doubts about the Taliban's intention, alluding to the "Trojan Horse strategy", but said that he needed to test the group's commitment.
Many in Kabul and government-controlled areas are concerned about a return of the Taliban if there were an eventual agreement.
Civil and women's rights campaigners are particularly concerned about the ultra-conservative religious group returning to government.
But US officials have said that so far the talks are aiming for an agreement on halting more bloodshed before the political elements are finalised.
“We have on the table right now a reduction in violence proposal that was negotiated between our ambassador and the Taliban," US Secretary of Defence Mark Esper said at the Munich Security Conference on Saturday. “It looks very promising.
“It’s my view as well that we have to give peace a chance, that the best if not the only way forward in Afghanistan is through a political agreement and that means taking some risk.”
Afghan Chief Executive Dr Abdullah Abdullah confirmed on Monday that the US peace agreement with the Taliban would be signed "in coming days" and said Afghan security forces should reduce violence in a goodwill gesture.
The anticipated seven-day reduction in violence, the longest in the war, would be a test of Taliban cohesion.
If successful, it will be followed by the signing of a deal between the US and the Taliban that would reduce US troop contingent “over time” to about 8,600. There are about 12,000 US troops in the country.
For years there were questions in Washington about the Taliban political leadership's ability to corral their bands of fighters to follow a ceasefire.
In 2018, the government and Taliban agreed to a three-day ceasefire for the Eid holidays, the first such halt in fighting since 2001.
The agreement saw Taliban fighters on the streets of Kabul and other Afghan cities hugging and taking selfies with soldiers and police.
The brief pause has not been repeated but showed that the Taliban command was able to make their fighters adhere to the ceasefire, as there was a major reduction in violence.