The US leader identified the kidnapped couple as Caitlan Coleman and Joshua Boyle, kidnapped during a backpacking trip in Afghanistan in 2012...
The US leader identified the kidnapped couple as Caitlan Coleman and Joshua Boyle, kidnapped during a backpacking trip in Afghanistan in 2012, and said their release was a "positive moment" for US relations with Pakistan.
"Ms Coleman gave birth to the couple's three children while they were in captivity," Trump said in a White House statement. "Today, they are free."
Trump said that the family had been held hostage by the Haqqani network, "a terrorist organization with ties to the Taliban."
The Haqqanis - whose head, Sirajuddin Haqqani, is also the Afghan Taliban's deputy leader -- are long thought to have links with Pakistan's shadowy military establishment. In 2011, Admiral Mike Mullen described them as a "veritable arm" of Pakistani intelligence.
Pakistan has been under increased pressure from Washington to crack down on alleged militant sanctuaries inside its borders after Trump lambasted the country in a televised address in August.
During the speech, Trump accused Islamabad of sheltering "agents of chaos" and suggested ties with Pakistan would be adjusted immediately but offered few details.
The Haqqani network has been accused of masterminding several high-profile terrorist attacks in the Afghan capital, including a massive truck bomb on May 31 which killed some 150 people, and have been known to kidnap Western hostages and smuggle them across the border into Pakistan.
The Pakistani military said Thursday the hostages had been recovered in Kurram district, part of Pakistan's semi-autonomous tribal belt, where militants such as the Haqqanis operated with impunity until the army intensified an operation there in 2014.
Kurram borders Nangarhar and Paktia provinces in Afghanistan. Both provinces are riven by militancy, with the Islamic State group gaining a foothold in Nangarhar and Paktia seen as a Haqqani stronghold.
The military said the five hostages were "safe and sound and are being repatriated to the country of their origin".
It gave no further details about the circumstances surrounding the hostages' recovery.
Boyle and Coleman appeared in a hostage video in December last year with two of their children pleading for their release.
The video was released after rumors swirled in Kabul that the government was planning to execute Anas Haqqani, son of the Haqqani network's founder, who has been held since 2014.
"This is a positive moment for our country's relationship with Pakistan. The Pakistani government's cooperation is a sign that it is honoring America's wishes for it to do more to provide security in the region," Trump said.
"We hope to see this type of cooperation and teamwork in helping secure the release of remaining hostages and in our future joint counterterrorism operations."
Secretary of State Rex Tillerson said the US expresses "deep gratitude" to Pakistan.
And Pakistan's military said: "The success underscores the importance of timely intelligence sharing and Pakistan's continued commitment towards fighting this menace through cooperation between two forces against a common enemy."
Afghanistan is rife with militants and organized criminal gangs who stage kidnappings for ransom, often targeting wealthy Afghans and foreigners, who have been ferried over the border into Pakistan's tribal belt.
The Taliban are also believed to be holding American Kevin King and Australian Timothy Weekes, both professors at the American University of Afghanistan, who were dragged from their vehicles in Kabul by gunmen in August last year.
US Special Operations forces conducted a secret raid authorised by then-President Barack Obama to rescue them, but the hostages were not there, the Pentagon said at the time.
They most recently appeared in a hostage video released in June this year.