The United States and the Taliban are moving forward on hashing out a peace deal that could pave the way to U.S. troops withdrawal from Afghanistan, according to the U.S. official in charge of negotiations. While this deal is still a long way from being finalized, a future deal could reportedly see the Taliban holding onto territory in Afghanistan through a cease-fire agreement.

Here's what we know

Zalmay Khalilzad is the chief U.S. negotiator who is trying to work on a peace deal with the Taliban. Representatives from both sides have been meeting in Qatar for the past week. Khalilzad flew back from Qatar to Afghanistan on Sunday to report on the progress of these talks.

"We have a draft of the framework that has to be fleshed out before it becomes an agreement," he told the New York Times. "The Taliban have committed, to our satisfaction, to do what is necessary that would prevent Afghanistan from ever becoming a platform for international terrorist groups or individuals."

He also said that the U.S. team "felt enough confidence that we said we need to get this fleshed out, and details need to be worked out."

According to the framework agreed to so far, the Taliban would promise to not allow the parts of Afghanistan it controls to become training grounds for terrorists. There would reportedly be some sort of enforcement mechanism to make sure that these promises were being kept, but it is not clear at this point what that might look like.

According to The Guardian, the Taliban currently controls about half of all the territory in Afghanistan. It is not clear yet how much, if any, of that territory the Taliban would be forced to give up if a deal is reached.

Khalilzad said that the talks in Qatar have been "more productive than they have been in the past," referencing years of without any progress between the U.S. and the Taliban.

A spokesman for the Taliban also said that the negotiations "saw progress," although he insisted that "until the issue of withdrawal of foreign forces from Afghanistan is agreed upon, progress in other issues is impossible."

What about the Taliban's demand?

However, according to a statement from current Afghan President Ashraf Ghani's office reported by the Washington Post, the discussions in Qatar had not touched on a key Taliban demand: A place in the current Afghan government. A document from Khalilzad's predecessor even talked about creating an interim government that would include the Taliban, although current Afghan leadership has denied that it would ever agree to such a deal.

The Taliban has also insisted throughout this process that U.S. troops leave before a cease-fire is reached, while U.S. and Afghan negotiators want to see a cease-fire before U.S. troops leave.

Before U.S. forces intervened after the Sept. 11, 2001, attacks, the Taliban controlled the country through a brutal and oppressive regime. Ghani assured his people on Monday that he would not accept a peace deal that would harm the rights they've secured since then.