The Taliban-tied Haqqani Network has threatened to kill an American hostage and her family unless the Afghanistan government halts its executions of Islamic radical prisoners.

A proof-of-life video released this week by the jihadists – the same group that held U.S. Army Sgt. Bowe Bergdahl - shows 31-year-old American Caitlan Coleman and her Canadian husband Joshua Boyle, who were kidnapped by the group in late 2012 while backpacking in the war-torn country.

The pair, who are believed to have had two children in captivity, are seen making desperate pleas to their governments to put pressure on the Afghanistan leadership to stop carrying out death sentences of imprisoned Taliban terrorists.

“We have been told that the Afghan government has executed some of their prisoners and that our captors are frightened of the idea of further executions,” Coleman, covered in black, says into the camera.

“Because of their fear, they are willing to kill us, willing to kill women and to kill children, to kill whoever in order to get these policies reversed or to take revenge.”

Coleman then asks her family to “do anything to help stop the depravity” of the killings. The family is being held at an unknown location and their health and wellbeing are not known.

Coleman was pregnant at the time they were captured, and according to a well-placed source, she has had a second son.

It is believed that the video was made a few months ago in response to Afghan officials hanging six Taliban prisoners in early May amid a blitz to rid the nation of terrorists. However, the decision by Haqqani to release the video this week comes on the heels of the ruling on Monday by an Afghan court to execute Anas Haqqani, the brother of the network’s notorious leader.

He was captured by U.S. officials while traveling through Qatar and Saudi Arabia in 2014 and he was handed over to the Afghan government for sentencing.

The Haqqani network has orchestrated a vast array of brutal attacks in Afghanistan in recent years, against both locals and the U.S. military, but unlike their Taliban associates, they are deemed to be more motivated by money than faith. That could help the U.S. get around its official policy of not dealing with terrorists. The Arab nation of Qatar took part in the talks that led to Bergdahl’s release.

A source told FoxNews.com that some hope arose earlier this year that at least some members of the family would be “released imminently,” but ultimately the deal fell through.

“Nothing has changed. They are hostages and nobody can get them home,” said the insider, noting that the Bergdahl and Iranian prisoner exchanges have made negotiations for the U.S government and the families far more difficult. “The 5-for-1 [swap for Bergdahl] and the Iran “non-ransom” made negotiations harder. We aren't getting them back for free, obviously, so the strategy is to pay as little as possible in gold and political capital through third parties. But we repeatedly inflated the cost of hostages and made this worse for ourselves.”

U.S. officials have acknowledged the video and are still in the process of verifying its authenticity. They have stated repeatedly that it is a top priority to bring home all Americans and their families being held against their will.

A spokesperson for the Canadian government told FoxNews.com that Ottawa is also aware of the video but will “not comment or release any information which may compromise or risk endangering the safety of Canadian citizens abroad.”

Several months after their disappearance in 2012, videos featuring the couple were emailed to the Coleman family by an Afghan man claiming to have Taliban ties but no direct involvement in their captivity. It wasn’t until June of 2014 that the families publicized the two videos – in which a gaunt Coleman was seen pleading to “my president, Barack Obama” for help. In those videos, Coleman referenced their baby but the child is not shown.

The decision to draw attention to their plight came following the release of Bergdahl, in the hopes that further awareness might lead to a successful negotiation. Family members also expressed disappointment that Boyle, Coleman and their baby were not freed as part of the deal.