Afghanistan’s president says he has ordered the release of three Taliban fighters in an effort to persuade the insurgent group to free a kidnapped American and Australian professor.

Timothy Weekes, an English teacher from Wagga Wagga in New South Wales, and Kevin King, from Pennsylvania, were abducted three years ago from outside American University of Afghanistan in Kabul by fighters in military uniform.

Ashraf Ghani, the Afghan president, said in a televised address on Tuesday that the three prisoners, from the Taliban-linked Haqqani network, would be released “conditionally in exchange” for the academics.

“We have decided to release these three Taliban prisoners who were arrested outside of Afghanistan,” Ghani said, adding that it was meant “to facilitate direct peace negotiations”.

If successful, the prisoner swap would be the first sign of diplomatic progress between the Taliban, the US-backed government of Afghanistan and the Trump administration since the US president abruptly cancelled peace talks in September – hours before he claimed Taliban leaders would be leaving for Camp David to finalise a deal.

By Tuesday evening in Kabul, there had been no confirmation the three Taliban figures had been freed, and if so, whether they were still in the country or had been flown overseas, possibly to Qatar, where the Taliban maintains a political office.

Neither the Taliban nor the Haqqani network had confirmed whether the western pair had been or would be released.

Weekes, 50, and King, 63, 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 dangerous as they “change the minds of society”.

Ghani said he made the “very hard but necessary” decision to release the Taliban prisoners, including Anas Haqqani – the brother of the Taliban’s deputy leader, – and a senior Haqqani leader, Hafiz Rashid.

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.

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.

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.

In a statement, the American University of Afghanistan said it welcomed the development and was “encouraged to hear reports of the possible release of our two colleagues, Kevin King and Timothy Weeks”.

The statement added that while the university was not part of any negotiations or discussions, it continues “to urge the immediate and safe return of our faculty members who have been held in captivity, away from their friends and families, for more than three years”.

The US and the Taliban were close to completing a deal to end the 18-year conflict until Trump scuttled the deal in a tweet in September.

Most of the terms of the provisional peace agreement were classified but they included the withdrawal of 5,000 American soldiers from five bases across Afghanistan by 2020. The Taliban would have agreed to renounce al-Qaida, fight the Islamic State group and stop jihadists from using the south Asian country as a safe haven.

The FBI last year announced a $1m reward for information leading to the release of King and Paul Edwin Overby, 76, an American writer thought to have been kidnapped in Afghanistan or Pakistan in 2014.