The foes have spent much of the past week in a sixth round of talks in Doha aimed at ending America's longest war, with US peace envoy Zalmay Khalilzad leading negotiations for Washington.

A potential deal would see America agree to withdraw its troops after more than 17 years in Afghanistan, in return for the Taliban guaranteeing the country never again becomes a safe haven for terror groups, as was the case with Al-Qaeda before the September 11, 2001 attacks.

The US also insists any deal includes a comprehensive and permanent ceasefire, and that the Taliban participate in an "intra-Afghan dialogue" with politicians and stakeholders from across Afghanistan.

Taliban political spokesman Suhail Shaheen told AFP the talks were taking a break for the first day of the holy month of Ramadan -- when Muslims fast during the day -- but would be resumed Tuesday.

He said discussions had become bogged down over the issue of when foreign forces might withdraw in return for the Taliban security guarantees.

The Taliban have said there is no point even discussing a ceasefire or an intra-Afghan dialogue before the US announces a troop withdrawal, whereas America wants to see all issues addressed at once.

Still, Shaheen said "some progress" had been made on the withdrawal issue and the question of Taliban security promises, but "both sides need more negotiations."

Sultan Barakat, the director of the Center for Conflict and Humanitarian Studies in Doha, also said the talks would resume Tuesday, and that they had made "good progress".

- 'Month of peace' -

At the end of a large peace summit in Kabul last week, President Ashraf Ghani offered the Taliban a ceasefire to begin on the first day of Ramadan, but the insurgents refused.

Ghani on Monday reiterated his call for the Taliban to respect demands from last week's "loya jirga" summit that saw thousands of tribal elders and Afghans meet in Kabul.

"Ramadan is a month of peace and reconciliation," Ghani said.

"I once again call on the Taliban to pay respect to this month and the demands of the people for peace and reconciliation reflected (in the Loya Jirga)."

The talks in Doha are complex, with interactions translated back and forth into Pashto and English, while negotiators often pause to confer with higher-ups.

Khalilzad in February sounded an optimistic tone, suggesting a deal was within reach by July, but it is not clear how much more time is needed for the two sides to come to an agreement.

Meanwhile, violence continues apace across Afghanistan.

On Sunday, at least 13 people were killed and dozens more wounded after a Taliban suicide bomber and several gunmen attacked a police headquarters in northern Afghanistan.