The warring parties are meeting in Doha on the second day of a three-day ceasefire to speed up stalled peace talks.
Taliban and Afghan government negotiators met in Qatar, warring parties say, after a long hiatus in peace talks between the two.
The development came on Friday, the second day of a three-day ceasefire announced by the Taliban for the Muslim holiday of Eid al-Fitr.
They began negotiations in September last year to find a way to end decades of war. But talks stalled after a few rounds, and violence has escalated since the United States began the final withdrawal of its troops from Afghanistan on May 1.
“The two sides discussed the current situation in the country and focused on accelerating the peace talks in Doha,” the negotiating team representing the Afghan government said on Twitter.
Taliban Politburo spokesman Mohammad Naeem posted a similar message on Twitter and added that the two sides agreed to continue talks after the Eid holiday.
Finding common ground between the two warring parties has been a top priority for Western capitals, especially Washington, which has announced that it will withdraw all U.S. troops by September to end its 20-year military presence. in Afghanistan.
The Taliban refused to attend a Washington-backed conference in Istanbul, Turkey last month, which was held in an attempt to speed up peace talks. The event was then postponed indefinitely.