Afghan President Ashraf Ghani reported "notable progress" in negotiations between Washington and the Taliban, which have now lasted over a year.

The prospective deal would see the US pull thousands of troops from Afghanistan, in return for which the Taliban would provide various security guarantees and launch eventual talks with the Kabul government.

"We would welcome any step that can lead to the reduction of violence," Stoltenberg said as he arrived for a meeting of NATO defence ministers, who will discuss the alliance's training and support mission in Afghanistan on Thursday.

A New York Times report citing Afghan and US officials said President Donald Trump has given conditional approval to a deal with the Taliban as he seeks to end America's longest war.

But progress remains fragile -- a deadly suicide attack in Kabul on Tuesday underlined the continuing threat of violence, and Stoltenberg warned the jihadists must make good on their promises.

"The Taliban has to demonstrate a real will and ability to deliver a reduction in violence to make it possible to have any progress towards a lasting and sustainable peace solution in Afghanistan," Stoltenberg said.

A de-facto ceasefire would enable the Americans to start withdrawing thousands of troops from Afghanistan, where between 12-13,000 are currently based.

The US and the Taliban have been on the brink of a breakthrough before, with a deal all but complete in September before Trump nixed it at the last moment amid continuing Taliban violence.