The Taliban say the gap is narrowing in talks with Washington's special peace envoy over a timetable for the withdrawal of US troops from Afghanistan.
The two sides are continuing to meet in Qatar, where the insurgent movement maintains a political office.
In a voice message sent Saturday to The Associated Press, the Taliban spokesman in Doha says both sides have offered new proposals for drawing down US and NATO forces.
This would be a significant initial step toward a deal to end nearly 18 years of war and America's longest military engagement.
US peace envoy Zalmay Khalilzad, however, continued to press for a cease fire, tweeting Friday: "It is time to put down arms."
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