United States President Donald Trump on Thursday said the recovery of the Canadian-American couple from Taliban captivity by Pakistan's was a "positive moment" for US relations with Pakistan.

The Pakistan government's cooperation is a sign that "it is honouring America's wishes for it to do more to provide security in the region”, Trump said in a White House statement.

Earlier, the army had announced that it had recovered "safe and sound" a family of foreign hostages — an American woman, her Canadian husband and their three children — from the Taliban captivity after it received and acted on intelligence shared by the United States (US).

The US president identified the 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, adding that “today, they are free”. “This is a positive moment for our country's relationship with Pakistan."

Trump said that the family had been held hostage by the Haqqani network, “a terrorist organisation with ties to the Taliban.”

“We hope to see this type of cooperation and teamwork in helping secure the release of remaining hostages and in our future joint counter-terrorism operations,” he maintained.

Secretary of State Rex Tillerson said the US expresses “deep gratitude” to Pakistan.

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 rumours 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.

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.