FILE - This combination of two photos taken from video released on June 21, 2017, by the Taliban spokesman Zabihullah Mujahid, shows kidnapped teachers Australian Timothy Weeks, top, and American Kevin King, who were abducted in Afghanistan in August 2016. King and Weeks were released Tuesday, Nov. 19, 2019, hours after the Afghan government freed three Taliban prisoners and sent them to Qatar. (AL-EMARA Taliban via AP, File)

FILE - This combination of two photos taken from video released on June 21, 2017, by the Taliban spokesman Zabihullah Mujahid, shows kidnapped teachers Australian Timothy Weeks, top, and American Kevin King, who were abducted in Afghanistan in August 2016. King and Weeks were released Tuesday, Nov. 19, 2019, hours after the Afghan government freed three Taliban prisoners and sent them to Qatar. (AL-EMARA Taliban via AP, File)

ISLAMABAD (AP) — The Taliban on Tuesday freed an American and an Australian held hostage since 2016 in exchange for three top Taliban figures — a move that the insurgent group asserted could help rekindle talks to end Afghanistan’s 18-year war.

The hostages — American Kevin King and Australian Timothy Weeks — were released in an area of southern Afghanistan heavily controlled by the Taliban, ending more than three years of captivity since they were abducted outside the American University in Kabul, where both had been professors.

A Taliban statement that followed the swap, which freed the younger brother of Sirajuddin Haqqani, the head of the fearsome Haqqani network, called the exchange a “confidence-building measure” that could help bring an end to Afghanistan’s endless war.

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Anas Haqqani, along with an uncle, Hajji Malik Khan, and a Haqqani lieutenant, Hafiz Rashid Khan, were released by the Afghan government on Monday and flown to Qatar, where the extremist group has a political office in the capital, Doha.

The U.S. State Department said in a statement that King and Weeks were in the care of the U.S. military, where they were recovering and would soon be reunited with their loved ones.

The two were released in southern Zabul province’s Naw Bahar district, a region largely under Taliban control, according to a Taliban official who spoke on condition of anonymity because he wasn’t authorized to talk to the media. King and Weeks were handed over to U.S. forces and transported from the area in a U.S. helicopter.

“We are so happy to hear that my brother has been freed and is on his way home to us,” said King’s sister, Stephanie Miller. “This has been a long and painful ordeal for our entire family, and his safe return has been our highest priority. We appreciate the support we have received and ask for privacy as we await Kevin’s safe return.”

Their freedom came hours after the Afghan government released the three Taliban prisoners, presumably after securing assurances from the Qatar government that they will remain in Qatar and not return to the battlefield.

In 2014 the Qatar government accepted five senior Taliban who were released from Guantanamo Bay prison by U.S. President Barak Obama in exchange for U.S. Sgt. Bowe Berdahl.

The five, including some accused of crimes that included orchestrating the slayings of 2,000 Shiite Muslims in northern Afghanistan, were forbidden from leaving Doha.

However, they were allowed to join the Taliban team negotiating directly with Washington’s peace envoy Zalmay Khalilzad. Anas Haqqani’s name was also put on the negotiation team even as he languished in an Afghan prison.

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Australian Prime Minister Scott Morrison expressed gratitude for the hostages’ release, saying on Twitter that Weeks’ family had “asked the Australian government to convey their relief that their long ordeal is over, and their gratitude to all those who have contributed to Tim’s safe return.”

Pakistani Prime Minister Imran Khan also welcomed the men’s release, saying he appreciates “steps taken by all involved to make it possible.” Pakistan wields some influence over the Taliban and has played a behind-the-scenes role in trying to restart peace talks.

Last week, Afghan President Ashraf Ghani announced what he called the “conditional release” of the three Taliban figures, saying in a live broadcast on state television that it was a difficult decision he felt he had to make in the interest of the Afghan people.

King’s family noted the “behind the scenes” efforts made by special envoy Khalilzad, U.S. Secretary of State Mike Pompeo and National Security Adviser Robert O’Brien to get Ghani on board with the prisoner swap. Pompeo and O’Brien made separate calls to Ghani on Monday, the Afghan government said.

In 2017, several months after their abduction, the Taliban released two videos showing the captives. A January 2017 video showed them appearing pale and gaunt. In a later video, King and Weeks looked healthier and said a deadline for their release had been set for June 16 that year.

Both said they were being treated well by the Taliban and appealed to their governments to help set them free. It was impossible to know whether they were forced to speak.

Subsequently, U.S. officials said that American forces had launched a rescue mission to free the two, but the captives were not found at the raided location.

In a statement on Tuesday, Pompeo called the prisoner exchange that led to the men’s release a “hopeful sign” that Afghanistan’s relentless war can soon come to an end.

The United States had been close to an agreement with the Taliban in September that would have paved the way for a U.S. troop withdrawal as well as direct talks between the Taliban and prominent Afghans, including representatives of the Afghan government, to negotiate an end to the war and map out a framework for a post-war Afghanistan. But a fresh wave of violence in the Afghan capital that killed a U.S. soldier brought those talks to a halt.

Ghani, in his discussions with Pompeo and O’Brien on Monday, said he wanted the prisoner swap to result in a reduction in violence and an all-out cease-fire, his spokesman said.

According to a U.S. State Department statement Tuesday, Pompeo told Ghani the United States was “committed to work closely together to address violence if the president’s decision does not produce the intended results.”

Southern Zabul province, where the two hostages were freed, is heavily controlled by the Taliban and vast parts of it have long been a no-go area for the government.

But according to the Taliban, an unofficial cease-fire is now being observed in three districts of the province — Shahjoy, Shahmatzo and Naw Bahar — possibly to facilitate the release of the two hostages.

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Associated Press writers Abdul Khaliq in Lashkar Gah, Afghanistan; Tameem Akhgar in Kabul, Afghanistan, and Matthew Lee in Washington contributed to this report.