Suhail Shaheen said the deal will also include guarantees that Afghanistan will not be used again as a staging arena for anti-American attacks, AP reported.
His remarks came during the second day of talks in the Qatari capital of Doha with US envoy Zalmay Khalilzad who has been trying to negotiate a resolution of the 17-year war in Afghanistan, America's longest.
"If we do not reach a solution in this round of talks, then we will in the next round of talks, but that is our target," Shaheen said.
He said the sides in the talks are for now sticking to the two-point agenda: US withdrawal and no-attacks guarantees.
Khalilzad arrived Monday for the talks in Doha and tweeted that that this could be "a significant moment" in the process.
Khalilzad's past rounds of talks with the Taliban focused on American troop withdrawal in exchange for guarantees of no attacks against the US but it was unclear how close he was on a deal on those issues.
He has also been expected to pressure the Taliban to hold direct talks with the Kabul government.