The Pakistani military rescued a kidnapped US-Canadian couple and their three children after receiving intelligence from the United States, Pakistan said today, nearly five years after the couple was kidnapped in Afghanistan.

American Caitlan Coleman, her Canadian husband Joshua Boyle and the children born in captivity were believed to be held by the Taliban-allied Haqqani network, which the United States has long accused Pakistan of not doing enough to fight.

Coleman and Boyle were kidnapped while backpacking in Afghanistan in 2012. Coleman was pregnant at the time, and a video released by the Taliban in December showed their two sons born while they were hostages.

Today's statement from the Pakistani army was the first mention of a third child.

The rescue came as Pakistan and the United States, uneasy allies in fighting Taliban and other Islamist extremists in the region, are experiencing one of the worst lows in relations.

Pakistan touted the success of the operation as proof of the strength of the alliance.

"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," the Pakistani army statement said. The family were released from "terrorist custody".

US intelligence agencies had been tracking the hostages and on Wednesday shared that they family had been moved across to Pakistan through Kurram tribal area border, the army said. No other details were immediately available.