ISLAMABAD -  The military said the captors of a US-Canadian family held by the Taliban fled on foot after troops shot at their vehicle’s tyres, as it offered a fuller account Friday of the operation to rescue the hostages.

American Caitlan Coleman and her Canadian husband Joshua Boyle, who were kidnapped while backpacking in Afghanistan in 2012 and had all three of their children in captivity, have left Pakistan after being freed, according to a US official.

The army said it launched the rescue after a tip-off from US intelligence that the family had been moved into Pakistan’s semi-autonomous tribal areas from across the border in Afghanistan.

Residents in the tribal districts of Kurram, where the operation took place, and North Waziristan told AFP they had seen drones flying in the skies above them for several days before the operation.

Major General Asif Ghafoor, military spokesman, said Pakistan was told by US intelligence at 4pm Wednesday that the hostages were on the move. “We sent our troops, traced the vehicle on the basis of intelligence sharing by 1900 hours yesterday (Wednesday) and recovered the hostages,” he said in televised comments late Thursday.

Pakistani forces had planned to intercept the vehicle at a security checkpoint in Kurram tribal district, a security source told AFP - but the militants drove it off the road.

Troops tried to stop the vehicle once it had travelled a few miles over the border. “But when the militants refused to halt, they shot out its tyres,” Ghafoor told AFP.

The militants “fled on foot”, leaving the family in the car, according to Ghafoor, who added that Pakistani soldiers had not wanted to risk injuring the hostages by firing on their fleeing captors.

Late Thursday a US military official told AFP the couple was hesitating to board a US military jet in Pakistan over Boyle’s concerns he could face American scrutiny over his previous marriage to the sister of a Guantanamo detainee.

In 2009 he was briefly married to Zaynab Khadr, the sister of Canadian-born Omar Khadr, who spent a decade at Guantanamo.

Canadian and US officials have said Boyle is not being investigated. A second US official confirmed the couple had left the country on condition of anonymity Friday afternoon, but gave no further details.

Some unnamed US and Canadian officials have cast doubt on Pakistan’s version of the rescue, hinting in North American media that the recovery was more of a “negotiated handover”.

A government source in Kabul told AFP they had informed the US and Canada in 2015 that the hostages had been transferred to Pakistan’s tribal areas. “It means Pakistan could have released them far earlier... But due to the tension with the US they felt it was the right moment,” the source continued.

A senior Taliban commander also denied the military’s account to AFP, saying the militants had released the hostages of their own volition after pressure on both sides of the border.

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.

Anas Haqqani is still believed to be in the custody of Afghan intelligence. On Friday, Afghan interior ministry spokesman Najib Danish told AFP there had been no prisoner swaps after questions over whether a deal had been struck to secure the hostages’ release.

In 2011, the chairman of the US Joint Chiefs of Staff at the time, Admiral Mike Mullen, described the Haqqani network as a “veritable arm” of Pakistani intelligence. The group has been accused of masterminding several high-profile terrorist attacks in the Afghan capital, including a massive truck bomb on May 31 that killed some 150 people.

They have been known to kidnap Western hostages and smuggle them across the Afghan border into Pakistan.

Kurram tribal district, where the hostages were recovered, borders Afghanistan’s Paktia province, a Haqqani stronghold, and Nangarhar province, where the Islamic State group has been gaining ground.

The Taliban are also thought to be holding American Kevin King and Australian Timothy Weekes, professors at the American University of Afghanistan who were dragged from vehicles in Kabul by gunmen last year.

Major General Asif Ghafoor, military spokesman for Pakistan’s army, told NBC News that the vehicle’s driver and another militant had escaped to a nearby refugee camp.

According to a Reuters, a second Pakistani security official, speaking on condition of anonymity, said US drones had been circling the town of Kohat, on the edge of the tribal areas on Wednesday, suggesting US cooperation included sophisticated surveillance inside Pakistan.

The US embassy in Pakistan declined to comment on the drone report.

Canada’s Toronto Star newspaper reported that Boyle told his parents that he asked to be taken to the Canadian High Commission in Islamabad after their rescue.

Boyle had been a staunch critic of the human rights abuses in the US war on terror after the attacks on Sept 11, 2001 and was previously married for a year to the sister of an inmate at the US military detention centre at Guantanamo Bay.

The Star reported that Boyle said he sustained minor shrapnel wounds during the shootout.