KABUL, Afghanistan — In the most substantial formal talks so far with the Taliban, United States officials discussed the future of the American military presence in Afghanistan and an offer of a three-month cease-fire during which the insurgents and the Afghan government could have negotiations, a senior American diplomat said on Thursday.

The diplomat, Zalmay Khalilzad, the Trump administration’s special representative in charge of the talks for Afghan reconciliation to end the 17-year war, briefed Afghan leaders in Kabul on two days of talks with the Taliban this week in the United Arab Emirates.

The discussions included representatives from the U.A.E., the host country; Saudi Arabia; and Pakistan — the only three nations that recognized the Taliban regime before it was toppled by the American invasion in 2001 and that still have varying degrees of influence over the insurgent group.

Mr. Khalilzad said in interviews with the Afghan TV channels ToloNews and Ariana that progress had been made in the talks even though Taliban representatives refused to meet with a delegation sent to the U.A.E. by the Afghan government.