In January 2017 the Taliban released a video showing Weeks - a teacher from Wagga Wagga, NSW - and King appearing pale and gaunt. In a second video, King and Weeks looked healthier and said a deadline for their release was set for June 16 that year.

Both said they were being treated well by the Taliban but that they remained prisoners and appealed to their governments to help set them free. It was not obvious from the videos whether they were forced to speak or did so willingly.

Subsequently, US officials said American forces had launched a rescue mission to free the two, but the captives were not found during the raid.

Foreign Minister Marise Payne's office was contacted for comment, but had not yet provide a response on Tuesday evening.

The prisoner exchange comes at a time when efforts were being made to revamp peace talks between the United States and the Taliban.

The Haqqani network has in recent years carried out large-scale militant attacks on civilians. It is believed to be based in Pakistan and is part of the Taliban in Afghanistan.

Anas Haqqani is the younger brother of Sirajuddin Haqqani, who is second-in-command in the Afghan Taliban hierarchy and leads the Haqqani network, considered to the deadliest faction of the Afghan Taliban.

A Taliban spokesman earlier this year said that the movement was determined to obtain Anas Haqqani's release and named him as a member of a negotiating team that would hold talks with US officials.

Ghani said authorities had been unable to discover where the Taliban were holding the two captive.

"Information suggests that their health while being held by the terrorists has deteriorated," he said.

Pakistani Prime Minister Imran Khan during a three-day visit to Washington in July that he would do his best to help release the American University professors.

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A Pakistani delegation, including the chief of the powerful Inter-Services Intelligence (ISI) spy agency was in Kabul to meet Afghan authorities on Monday. A senior Pakistani official in Islamabad said the excahnge of prisoners was discussed by the delegation.

According to Afghan officials, the next round of talks between the Taliban and Afghan representatives is slated to be held this month in Beijing.