The Taliban handed two Western hostages over to U.S. forces in southern Afghanistan Tuesday, three years after they were abducted, in a swap for three high-ranking insurgent prisoners that could boost peace talks.

The exchange of American Kevin King and Australian Timothy Weeks for the militants -- including Anas Haqqani, brother to the Taliban's deputy leader -- was welcomed by both the United States and the insurgents.

U.S. Secretary of State Mike Pompeo said the releases "give us hope for the success of intra-Afghan peace negotiations, which the United States stands ready to support."

King and Weeks, both professors at the American University in Kabul, were kidnapped by gunmen wearing military uniforms in the heart of Afghan capital in August 2016.

They later appeared looking haggard in a Taliban hostage video, with the insurgents going on to say that King was in poor health.

On Tuesday morning, they were driven by car to Nawbahar district in Zabul, a southern province bordering Pakistan, an insurgent source told AFP.

They were freed at around 10:00 a.m. and flown out of Zabul on American helicopters, according to a local police source.

The insurgents were released in Doha, where the Taliban maintain a political office, a tweet from their spokesman in the Qatari capital Suhail Shaheen confirmed.

'A step forward'

The swap could herald a breakthrough in stalled efforts to bring the Taliban to the negotiating table with the Kabul government and begin work towards a political settlement ending their 18-year insurgency.

Mujahid described the exchange as "a step forward in good-will and confidence-building measures that can aid the peace process".

The U.S. welcomed the exchange and revealed the two hostages had suffered "significant hardship".

"We pray for the full recovery of both men," said White House Press Secretary Stephanie Grisham.

"We thank the Afghan government for its actions, in the spirit of our partnership that enabled the freeing of the hostages."

When Afghan President Ashraf Ghani first announced the potential exchange on November 12, he said that Kabul had ensured the militants would not return to the front line.

And he said he hoped the swap would "pave the way" for unofficial direct talks between his government and the Taliban, who have long refused to negotiate with Kabul.

Anas Haqqani, whose older brother Sirajuddin is the deputy Taliban leader and head of the Haqqani network, one of the militant group's deadliest factions, was seized in 2014.

Afghan authorities accuse Anas of being a high-level player in the network. The Taliban has long demanded his release, insisting he was a student.

The other two freed Taliban were Haji Mali Khan, believed to be the uncle of Sirajuddin Haqqani, and Abdul Rashid, said to be the brother of Mohammad Nabi Omari, a member of the Taliban's political office in Qatar.

Mujahid said the Taliban had also released 10 Afghan soldiers along with the Western hostages.

Australian relief

"We are profoundly pleased and relieved," Australian Prime Minister Scott Morrison said in a statement, adding that Weeks' family had asked the government to convey their relief and gratitude.

Since September 2018 Washington and the Taliban had been holding direct talks, seeking an agreement for U.S. troops to begin leaving Afghanistan and the militants start negotiations with Kabul.

They were on the verge of a deal when U.S. President Donald Trump scuttled the talks in September, citing Taliban violence.

Most observers agree that a political pact is the only way towards lasting peace in Afghanistan.

"We see these developments as hopeful signs that the Afghan war, a terrible and costly conflict that has lasted 40 years, may soon conclude through a political settlement," Pompeo said.

Pakistan's Prime Minister Imran Khan, whose government had helped facilitate the talks between the insurgents and Washington, also said he hoped the release would give a "boost of confidence" to all sides to re-engage.