In comments given to the New York Times and confirmed to CNN by the US Embassy in Kabul, Zalmay Khalilzad said the framework for peace would see the insurgent group vow to prevent the country from being used as a hub for terrorism in return for a US military withdrawal.
Acting Secretary of Defense Patrick Shanahan told reporters Monday that the United States talks with the Taliban were "encouraging", but when asked if he had been "tasked to be prepared for a full withdrawal", he replied, "I have not".
The U.S. and the Taliban have agreed to a draft framework for a peace agreement that could pave the pay for a U.S. military withdrawal from the country, said the chief American envoy to the country. In December 2018, during the talks at Abu Dhabi, sources tell WION that representatives of Saudi Arab had persuaded the Taliban to meet with the Afghan government in Saudi Arabia, an offer which the Taliban had refused to take.
According to the Associated Press, the president added, "There are values that are not disputable, such as national unity, national sovereignty and territorial integrity".
He told Afghan media that Washington and the insurgents had "agreed to agreements in principle on a couple of very important issues", and said Afghans must "seize the opportunity", according to comments released by the USA embassy in Kabul.
The militants are negotiating from a position of strength: they have the upper hand on the battlefield, and US President Donald Trump's reported eagerness to start withdrawing troops from Afghanistan is weighing heavy on the discussions.
"We want peace, we want it fast but we want it with a plan", he said.
The Trump administration's strategy has been to put pressure on the Taliban to negotiate with the Afghan government.
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In a statement issued by the Presidential Palace, Ghani's office said Khalilzad quashed rumors of talks around the future structure of Afghanistan's system with the Taliban and that there was no truth in reports of an interim government.
During his address, Ghani noted that US and other foreign forces remain in the country because they are still needed.
As well as the withdrawal of troops, the official said progress was made on addressing US concerns that Afghanistan is not used as a base by al Qaeda or Islamic State for attacks against the United States and its allies.
The Taliban have insisted foreign troops must pull out. Shortly after assuming office, however, he was convinced to stay, and even increased the number of USA troops in the country by some 4,000.
"There is a lot more work to be done before we can say we have succeeded in our efforts but I believe for the first time I can say that we have made significant progress", Khalilzad said in a statement.
The group believes that its Islamic government is the only legitimate form of rule in Afghanistan, and that, as Mullah Omar, the Taliban's founder who died in 2013, said, "We have come out for the goal of sacrificing in the path of Allah and establishing the law of the Allah on His servants".
The comments by special envoy Zalmay Khalilzad to the New York Times are the clearest signal yet from a USA official that talks between Washington and the terrorists are progressing, igniting hopes of a breakthrough in the grinding 17-year conflict.
On Friday, Mr Ghani said more than 45,000 members of the country's security forces had been killed since he became leader in 2014.