The US is in sober discussions with the Taliban for the first time in 19 years to end the war in Afghanistan, President Donald Trump has said as he touts his administration's talks with the militant group.

The hopeful tone comes hours after US Special delegate for Afghanistan Reconciliation Ambassador Zalmay Khalilzad protected his talks with the Taliban and caution against a rush to judgment.

While Khalilzad said his almost week-long meetings with Taliban officials yield "significant progress," Afghan President Ghani has spoken concern about the US troop removal from the war-torn country.

"I can't tell you that this is a guarantee because we are going into close to 19 years in being in Afghanistan and for the first time, they are talking about settling, they are talking about making an accord and we bring our people back home if that happens," Trump told reporters at the White House.

"We will see what happens but they are in very serious negotiations for the first time," he said.

Early this week, Khalilzad announce that he has reached a draft peace structure after six days of talks in Qatar. As per the draft framework, the Taliban will deny safe haven to terrorist groups. This is based on the considerate that the Taliban must enter into direct talks with Kabul and, at the same time, agree to a ceasefire.

Meanwhile, a media has said the Trump management is unlikely to order the removal of troops from Afghanistan without a complete cease-fire agreement with the Taliban and a political road map for peace.

Based on interviews with unidentified senior administration officials, The Washington Post in a news report said that "no withdrawal will occur until a complete cease-fire and a political road map for peace have been negotiated" between the militants and the Afghans.