The Taliban are planning to present a written peace proposal to the Afghan government side as soon as next month, a spokesman for the group said.
"The peace talks and process will be accelerated in the coming days ... and they are expected to enter an important stage, naturally it will be about peace plans," Taliban spokesperson Zabihullah Mujahid told Reuters on Monday.
"Possibly it will take a month to reach that stage when both sides will share their written peace plan," he said, adding that the latest round of talks was at a critical juncture.
"Although we (Taliban) have the upper hand on the battlefield, we are very serious about talks and dialogue."
Last week US forces vacated Bagram Air Base as part of an understanding with the Taliban.
While the transfer of Bagram Air Base to the Afghan army added momentum to a Taliban drive to seize control over new districts, Taliban leaders renewed the long-stalled talks with Afghan government envoys in Qatar's capital Doha last week.
Meanwhile, President Ashraf Ghani said that the Afghanistan government will never surrender to the Taliban.
Pointing out that the responsibility for the bloodshed and destruction falls on the Taliban and their supporters, the Afghan president stressed that there was no will to surrender to the Taliban.
He told a cabinet meeting on Tuesday that there was no deal and no will to surrender to the Taliban.
Ghani added the Taliban's wish to see the government surrender will never come true.
As the latest development, Germany said on Tuesday that it has closed its consulate general in Mazar-i-Sharif in northern Afghanistan in the course of the international military withdrawal.
KI