"Of course we don't seek a permanent military presence in Afghanistan", the official said in the capital Kabul. "We would like to leave a good legacy". "The world has accepted Pakistan's stance on the peace process" he said.
"The Taliban have committed, to our satisfaction, to do what is necessary that would prevent Afghanistan from ever becoming a platform for worldwide terrorist groups or individuals", he told the newspaper, adding that the USA team "felt enough confidence that we said we need to get this fleshed out, and details need to be worked out".
U.S. special envoy Zalmay Khalilzad has hailed "significant progress" in finding a solution to end Afghanistan's long-running war.
"The Taliban have committed, to our satisfaction, to do what is necessary that would prevent Afghanistan from ever becoming a platform for worldwide terrorist groups or individuals", he said.
USA forces in 2001 toppled Afghanistan's Taliban leaders who had harbored al Qaeda militants responsible for the September 11 attacks on the United States that killed about 3,000 people.
The source said the Taliban will not agree to a ceasefire without the United States committing to a full troop withdrawal, but the Americans want any withdrawal to be conditional on the ceasefire holding.
"It's encouraging", Shanahan, who said he had been briefed on the talks, told reporters outside the Pentagon before meeting NATO Secretary General Jens Stoltenberg.
A former Taliban leader said despite a agreement for an 18-month withdrawal, he predicted intense fighting ahead.
But president Ghani, in turn, apparently tried to assure the Afghan people that no deal would be made without Kabul's awareness and full participation in negotiations with the resurgent movement.More news: Super Blood Wolf Moon treks through Sunday night sky
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US President Donald Trump's clear eagerness to end America's longest war has also weighed heavy on the discussions, and Ghani warned against rushing into a deal, citing violence following the Soviet withdrawal in 1989. Trump last month rebuffed top advisers and made a decision to pull US troops out of Syria as well.
USA special envoy Zalmay Khalilzad - who has been leading the negotiations - arrived in Afghanistan late Sunday to update officials including Ghani on the progress made.
Both U.S. officials and the hardline Islamic group hailed progress after the talks on Saturday with Khalilzad.
The talks led by US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad were aimed at finding a negotiated settlement to the 17-year conflict which has gripped Afghanistan following the fall of Taliban regime in 2001.
The 14,000 US troops in Afghanistan are part of a NATO-led mission and a USA counter-terrorism mission largely directed at groups such as Islamic State and al Qaeda.
Some 8,000 troops from 38 other countries including Australia are participating in the operation, known as Resolute Support. The U.S. invaded Afghanistan after the September 11, 2001, attacks to topple the Taliban, who were harbouring Osama bin Laden and al-Qaeda.
"That is why we came to Afghanistan in the first place", the official said.
Khalilzad will stay in a Kabul for more talks with the Afghan government Monday, and there are discussions that Khalilzad may go back to Afghanistan in early February.
"The issue of interim government is completely incorrect and that's not within my authority".
Ghani and Khalilzad met late on Sunday in Kabul. "We have a draft of the framework that has to be fleshed out before it becomes an agreement", said Khalilzad as quoted by the New York Times in a report on Monday.