Peace talks between U.S. negotiators and Taliban representatives in Doha, Qatar, have been interrupted to mark the beginning of Ramadan.
The two sides are apparently at loggerheads over the key sticking point of when foreign forces might leave Afghanistan.
The two sides have been involved for much of the past week in a sixth round of negotiations aimed at ending the almost 18-year war -- the United States' longest ever -- but the Taliban says talks have become bogged down.
Taliban political spokesman Suhail Shaheen tweeted that the talks were pausing for the first day of the holy month of Ramadan -- when Muslims fast during the day -- but would be resumed "the following day."
Shaheen told AFP news agency late on May 5 that talks hit an impasse over when foreign forces would depart Afghanistan.
Before agreeing to any withdrawal, Washington is demanding that militants establish security guarantees, a cease-fire, and make other commitments including an "intra-Afghan" dialogue with the Kabul government and other Afghan representatives.
The Taliban has said it will not take any of these steps until the United States announces a withdrawal timeline.
At the end of a wide-ranging peace gathering in Kabul last week, President Ashraf Ghani offered the Taliban a cease-fire to begin on the first day of Ramadan, but the militants rejected it.
Ghani on May 6 reiterated his call for the Taliban to observe demands from last week's gathering that saw thousands of tribal elders and Afghans meet in Kabul.
At least 13 people were killed and dozens more wounded on May 5 after a Taliban suicide bomber and several gunmen attacked a police headquarters in the northern Afghan city of Pul-e Khumri.