The talks are expected to resume in February but former diplomats said India should watch out of the proxy masters of the Taliban in the Pakistani military establishment.
Despite the progress on a pact, violence is widely expected to continue, with the Taliban mounting daily attacks against the Afghan government and its security forces.
The U.S. official said progress was made on addressing core U.S. concerns that Afghanistan will not be used as a base by al Qaeda or Islamic State for attacks against the United States and its allies.
The Afghan president's office says USA peace envoy Zalmay Khalilzad shared details of his recent talks with the Taliban in Qatar with President Ashraf Ghani and other government officials.
Both the Taliban and the United States touted "progress" over the weekend, and the New York Times cited Washington's special envoy Zalmay Khalilzad on Monday as saying they have formed "a draft of a framework", though he warned details need to be fleshed out and major sticking points remain.
Monday's statement from Mr Ghani's office also claimed that the Taliban demanded from Mr Khalilzad the withdrawal of all foreign troops from Afghanistan, but that there was also no agreement on that issue.
There was headway on one topic, Khalilzad told the New York Times.
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The Hezbollah leader regularly addressed his supporters and made TV appearances about pressing issues in the region and Lebanon. Nasrallah smiled smugly as he said: "One of the tunnels discovered in recent weeks is 13 or 14 years old".
Khalilzad flew back from Qatar to Afghanistan on Sunday to report on the progress of these talks.
"There will need to be clear, hard assurances that any troop withdrawals take place only after the Taliban has begun talks with the Afghan government", Kugelman continued.
When will American-led forces be withdrawn from Afghanistan?
The statements also said Ghani thanked Khalilzad for his efforts and praised U.S. endeavors to restart negotiations between the Afghan government and the Taliban.
With Khalilzad and his boss U.S. Secretary of State Mike Pompeo, as well Taliban officials, hailing progress towards ending America's longest war, he must now win over President Ashraf Ghani - whose government the Taliban have so far kept out of the process.
The points of contention include a ceasefire, a timetable for the withdrawal of foreign troops, and the Taliban's ongoing refusal to speak to Kabul.
Ghani said in a televised address that the presence of foreign forces was based on an worldwide agreement and they will not be required forever.
Trump is planning to withdraw more than 5,000 of the 14,000 USA troops in Afghanistan, a US official said in December, in the latest sign that the US president's patience is thinning with America's longest war and overseas military interventions.
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Ghani has called for talks before, and outlined a peace plan past year which included a ceasefire and bringing the insurgents into mainstream politics.
Afghan President Ashraf Ghani in turn assured his people Monday that no deals would be made without Kabul's awareness or participation.
"My role is to facilitate" such talks between the insurgents and Kabul, Khalilzad was quoted as saying.
The Taliban have insisted foreign troops must pull out.
Australian combat troops were withdrawn in December 2013, but 400 personnel remain in Afghanistan as trainers and advisers.
Ghani, who addressed a panel at the World Economic Forum on January 24, disclosed new figures on casualties of Afghan forces by saying that more than 45,000 Afghan security personnel have lost their lives since he took office in September 2014.
The Taliban and USA officials have agreed to continue negotiations, though no date has been publicly announced.
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The agency added that role of "others" along with Mishra were also being probed for keeping the PE pending. The CBI will call all the accused to record their statements soon.