President Donald Trump would still have to formally approve the agreement and finalization of details is expected at this week's Munich Security Conference, where Esper and Pompeo will meet with Afghan President Ashaf Ghani.
Citing Afghan and USA officials, the New York Times has reported that President Donald Trump had given conditional approval to a deal with the Taliban to allow him to start withdrawing USA troops.
"We've said all along that the best.solution in Afghanistan is a political agreement", he added.
A US defense official cautioned that, even with Taliban leaders pledging a seven-day reduction in violence, attacks would be likely to continue because of the many splinter groups in Afghanistan.More news: Yellow weather warning for the East of England as storm Dennis approaches
"It is our view that seven days for now is sufficient but in all things our approach to this process will be conditions based, I will say it again, conditions based", Esper said.
Speaking at the same North Atlantic Treaty Organisation summit in Brussels attended by Esper, the secretary-general said the militants "need to demonstrate that they are both willing and capable to deliver a reduction of violence and contribute to peace in good faith".
The announcement came a day after Afghan President Ashraf Ghani reported "notable progress" in negotiations with the Islamist insurgents.
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"That doesn't mean we'll have one but we'll know over the next two weeks", he said.
The prospective deal would see the US pull thousands of troops from Afghanistan, while the Taliban would provide security guarantees and launch eventual talks with the Western-backed government in Kabul.
The U.S. and the Taliban may soon reach an agreement aimed at ending the 19-year war in Afghanistan, Defense Secretary Mark Esper said. "This time around will be longer and a lot more complex", Kugelman said.
They have previously said a ceasefire could blunt their battlefield momentum if the USA or Kabul renege on their promises. But the militants continued to refuse to hold official talks with the Afghan government, whom they dismissed as American "puppets".More news: US Space Force says mystery Russian craft tracking American spy satellites
"Given the messy Afghan political situation, including a prolonged election crisis and deep rivalries between powerful factions", Kugelman said, "it's going to be a tall order to launch much less conclude a successful peace process resulting in a power-sharing deal with the Taliban".