Afghan government officials and members of the Taliban have held two days of talks in Doha.
Few details emerged after the closed-door talks ended on May 3 in the Qatari city.
One Taliban participant in the talks told Reuters by telephone late on May 3 that an eight-member Taliban delegation, headed by Sher Mohammad Abbas Stanekzai, had held direct dialogue with Afghan officials.
He said the two sides discussed a possible cease-fire but ultimately disagreed over the continued presence of U.S. troops in the country.
The Taliban said they would not stop fighting until all foreign forces left Afghanistan, he said.
The government delegation argued that most foreigners had already left and only trainers remained, who would also leave if the Taliban stopped fighting, he said.
The talks ended with no agreement except to hold another meeting in the United Arab Emirates "probably next month."
The Taliban recently launched an offensive in northern Afghanistan that brought its fighters to the outskirts of Kunduz city, a provincial capital.
Based on reporting by Reuters