James and Lyn Coleman, who live in Pennsylvania, believe the insurgent group is holding their daughter, Caitlan, her Canadian-born husband Joshua Boyle and two sons, to whom she gave birth in captivity.
"We desperately want to be with and old our daughter and grandsons, whom we long to meet and care for," said Coleman in a short video, sitting next to his wife, whose hair was covered in a black veil.
He asked them "to show mercy" and release the family. "Please allow Caity and her family to come home," he said.
"May God reward your good deed and see that it is returned to you in kind, Eid Mubarak."
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The Muslim festival of Eid al-Fitr, which marks the end of the fasting month of Ramadan -- traditionally a time of mercy -- is due to begin next week.
The Colemans last saw their daughter in July 2012, when she set off for Russia on a hiking trip with Boyle that took them through Central Asia and ultimately into war-torn Afghanistan.
The couple were last seen in a video emailed to her parents in 2013 in which they asked the US government and their families to secure their release.
The Colemans made the video public after Bowe Bergdahl, a US Army sergeant held captive for five years in Afghanistan, was freed in a prisoner swap.
President Barack Obama last month said that he was according greater powers to the US military to go after the Taliban and work more closely with Afghan government troops, ratching up a 15-year conflict he has vowed to end.