President Ghani’s spokesman Sediq Sediqqi, said Saturday that if the Taliban accepts the US proposal for a ceasefire, direct and face-to-face talks will begin between the Afghan government and the Taliban.

Sediqqi said that US President Donald Trump advocated a peace “owned by the Afghan government” during his Thursday visit with Afghanistan’s President Ghani at Bagram airfield.

“Our hope is that the Taliban will work to accept their (US) ceasefire. If they (Taliban) are really committed to giving up the war - in our opinion - the best opportunity is for them to accept that opportunity,” said President Ghani’s spokesman Sediq Sediqqi.

During his unexpected visit to Afghanistan on Thursday, Trump said, referring to the Taliban:“ We’re saying it has to be a ceasefire. And they don’t want to do a ceasefire, but now they do want to do a ceasefire, I believe... and we’ll see what happens.”

But former Taliban members in Kabul say the group will not agree to a ceasefire unless a peace deal is first signed between the United States and the Taliban--before intra-Afghan dialogue has started.

“The agreement will be signed first, then a ceasefire will be announced. The Taliban's big secret and reason for signing an agreement is to make sure that the group has a guarantee from the US – build trust and then declare a ceasefire,” said Mawolana Jalaluddin Shinwari, a former official during the Taliban’s regime.

“The Taliban's reaction to Mr. Trump's trip [to Afghanistan] was also very strange; they just said that Mr. Trump had said this beforehand,” said Humayun Jarir, a member of Hizb-e-Islami party led by Gulbuddin Hekmatyar.

NATO Secretary General Jens Stoltenberg at a press conference on Friday said he welcomes “contacts” between the United States and the Taliban and said that the US consults with NATO allies “regularly” regarding peace efforts in Afghanistan.

Pompeo has discussed, briefed Allies. Ambassador Khalilzad has briefed Allies, discussed this with Allies. And we are consulting all the time because it is not only US in Afghanistan, but we have to remember there are also many non-US troops in Afghanistan,” he said.

Stoltenberg said that Afghanistan “remains our biggest military operation outside Europe” and he repeated NATO’s current mission is “to prevent Afghanistan from once again becoming a safe haven for international terrorists.”

Some sources familiar with the peace talks say US officials are engaged in informal talks with Taliban officials in Doha to facilitate the formal resumption of bilateral talks.