The meeting took place on Monday as Ghani embarked on a two-nation trip earlier in the day to Qatar and Kuwait, reports TOLO News.

In a series of tweets after the meeting, Khalilzad said: "I told the President that Afghans should not let the opportunity for peace to slip away. He said he supports the Islamic Republic negotiators doing their work as long as it takes. I said I'm encouraged by what I heard from all sides, including the two teams' commitment to peace.

"We call on all nations, especially the neighbours and other key players, to do the same.

"A significant reduction in violence will save lives; increase trust; broaden support for peace; and help the negotiating teams make progress at a faster pace. This is what the Afghan people want. And the US stands with them.

"Violence is too high, and too many Afghans are dying... We are pressing for a significant reduction in violence that will lead to a permanent and comprehensive ceasefire.

"General Miller and I affirmed ongoing US support to Afghanistan, our partnership, and a peace process meant to produce a political settlement and an end to decades of war."

Also on Monday, Taliban spokesman Mohammad Naeem said that Khalilzad and Gen. Miller met the militant group's deputy leader Abdul Ghani Baradar and discussed the implementation of the Doha agreement, calling it "significant for the resolution of Afghanistan issue".

The opening ceremony for the intra-Afghan talks was held on September 12, but the two sides were yet to begin direct negotiations, TOLO News reported.

Their contact group have so far held seven meetings to discuss procedural rules for the talks.

The two sides have yet to agree on two matters: the religious basis for the talks and the relevance of the US-Taliban deal.