The deal could end the war in Afghanistan (Picture: PA).
A US envoy showed the draft of a US-Taliban agreement to Afghan leaders on Monday after declaring they were "at the threshold" of a deal to end America's longest war, an official said.
Presidential adviser Waheed Omer in a Twitter post said envoy Zalmay Khalilzad again met with President Ashraf Ghani after an initial meeting on Sunday evening upon arriving from Qatar, where the ninth round of US-Taliban talks ended without a final agreement.
The agreement with the Taliban "will reduce violence and open the door for Afghans to sit together to negotiate an honourable and sustainable peace," the Afghan-born Mr Khalilzad said before his Kabul arrival.
A US official with the negotiation team added that "any potential peace deal will not be based on blind trust, but will instead contain clear commitments that are subject to our monitoring and verification".
The official spoke on condition of anonymity because they were not authorised to discuss the matter with the media.
The official added that a deal would lead to "intra-Afghan negotiations where the Taliban will sit with other Afghans and together they will commit to a permanent and comprehensive ceasefire".
The Taliban want all of the estimated 20,000 US and NATO forces to leave the country and already portray their departure as the insurgents' victory.
"We are on the verge of ending the invasion and reaching a peaceful solution for Afghanistan," the Taliban spokesman in Qatar, Suhail Shaheen, said over the weekend.
For its part, the US seeks Taliban assurances that Afghanistan will not be a safe haven for extremist groups to plan and launch global terror attacks.
A ceasefire also has been discussed.
While the deal could end 18 years of fighting between US forces and the Taliban, the situation in Afghanistan is far from stable.
At the weekend, the Taliban attacked the capitals of Kunduz and Baghlan provinces in the north over the weekend and the insurgent group is believed to be at its strongest since the US-led invasion to topple its government after the 9/11 attacks.
The Taliban now control or hold sway over roughly half of Afghanistan and have stepped up attacks in recent months to strengthen their negotiating position.
Afghan's presidency was expected to brief the media Monday afternoon on Mr Khalilzad's visit.
The Afghan government has been shut out of the negotiations as the Taliban dismiss it as a "US puppet", but intra-Afghan talks that include the government are meant to follow a US-Taliban deal.
Unrest continued Monday outside the Baghlan capital of Puli Khumri as the Taliban blocked the main road leading south to Kabul with fuel tanker trucks, opening fire on any security forces that tried to approach, provincial council member Mabobullah Ghafari said.
The Taliban also blocked the two main roads heading north from Puli Khumri as gun battles continued, he said.
The situation inside the city was calm but residents remained fearful of attack, he added.
At least 47 wounded people had been taken to hospitals since the attack began on Sunday morning, said Jawed Basharat, spokesman for the provincial police chief.
The interior ministry later said at least 51 Taliban fighters, seven civilians and six members of security forces had been killed, and said the Taliban soon would be eliminated from the area.
Kunduz was back to normal, the ministry added.
Separately on Sunday night, six pro-government soldiers were killed and three were wounded when Taliban fighters ambushed their patrol in Qarabagh district of eastern Ghazni province, said Arif Noori, spokesman for the governor.