Asked if the Afghan people were ready to accept a Taliban deal with the United States, the High Peace Council member said common Afghans were in favor of an agreement as they wanted an end to the conflict and desired to see foreign forces quit Afghanistan.
So far this year, 14 American troops have died in Afghanistan in combat.
That attack again raised fears among Afghans that a U.S. -Taliban deal will bring little peace for long-suffering civilians who have died by the tens of thousands in the past decade alone.
The Taliban have claimed responsibility for Wednesday's killing of two USA soldiers in northern Afghanistan.
Zalmay Khalilzad, an Afghan-born US diplomat who has been leading the negotiations with the Taliban since previous year is scheduled to travel to Kabul after his talks with the Taliban officials.
Afghanistan will not be significantly affected even if 5,000 US forces leave in the next five months, an option that has been under discussion, he added in a nationally televised interview.
Later, a USA official said the two service members died in combat from small-arms fire without providing further information.
The Taliban now control more territory than at any point since the United States bombed them out of power in 2001 for sheltering Al-Qaeda, the group blamed for the September 11 attacks on the United States. "The Taliban does not respect the Afghan government", Trump said earlier this week, adding: "It is a unsafe place and we have to keep an eye on it".