An Australian and an American professor in Taliban custody who were supposed to be freed in a prisoner exchange this week are still yet to be released, according to a spokesman from the militant group.

The Afghan government said earlier this week it would “conditionally release” three militants from the Taliban-linked Haqqani network as part of an apparent exchange for Timothy Weekes, 50, and Kevin King, 63, who were kidnapped by the group in Kabul in 2016.

Ashraf Ghani, the Afghan president, ordered the release of the prominent Taliban figures on Tuesday, with the return of Weekes and King expected to be confirmed shortly after.

On Thursday a Taliban spokesman confirmed the group had not received its prisoners and that the western pair were still in their custody. “The three [Taliban] people have not been handed over to us, and we have not freed our prisoners yet,” Zabihullah Mujahid told Agence France-Presse.

Diplomats in Kabul had first flagged an unexplained problem with the deal on Wednesday. The Australian government had said in a statement the same day it was still hoping for their imminent release.

The Australian government and the US state department have been contacted for comment.

The prisoner swap was viewed as a possible step towards restarting peace negotiations between the Taliban and the US government, which were in their final stages in September before being abruptly cancelled by Donald Trump, after an attack by the militant group that killed 12 people, including a US soldier.

Weekes, from the New South Wales town of Wagga Wagga, and King, from Pennsylvania, were seized at gunpoint from a car in August 2016. US Navy Seals conducted a raid to free them days later, descending on a militant hideout in the mountains of eastern Afghanistan, but the men had been moved hours earlier, according to reports.

The pair appeared looking gaunt and weathered in a video released in January 2017 begging their parents to ask the US government to negotiate for their release. They appeared in a second video later that year, setting a June 2017 deadline for their release, and the Taliban released a statement in October of that year claiming King was suffering from a “dangerous heart and kidney disease”.

“We have tried to treat him from time to time, but we do not have medical facilities as we are in a war situation,” the Taliban statement said.

A Taliban commander in eastern Afghanistan previously told the Guardian the group considered teachers at the American University of Afghanistan dangerous as they “change the minds of society”.

The Haqqani group predates the Taliban but has become integrated into its structure, and is suspected of having carried out some of the most brutal and indiscriminate attacks over the course of the nearly two decades of war that have followed the 2001 US-led invasion.

One of the prisoners scheduled to be freed, Anas Haqqani, was arrested in Bahrain in 2014 and charged with raising funds “from individuals from Arab countries” and recruitment through social media. He was sentenced to death and his release has long been demanded by the Taliban.

Another, Hafiz Rashid, was the Haqqani network commander for south-eastern Afghanistan and accused of being in charge of selecting targets and providing equipment for suicide bombers.

The third prisoner, Haji Mali Khan, was also a senior commander of the Haqqani network.