Parents of American Held Hostage by Taliban Say She's Had Second Child in Captivity Caitlan Coleman, 29, has been held with Canadian husband for more than 3 years.

 -- The parents of an American woman held hostage for almost four years in South Asia by Islamist militants said today that their daughter has given birth to a second son in captivity.

James Coleman and his wife Lynda of Stewartstown, Penn., revealed that a second grandchild was born to their daughter Caitlan Coleman, 29, in an interview with Circa, saying the news came in a letter they received last November.

The parents also made a new video in which they deliver a direct Ramadan plea to new Taliban leader Mawlawi Haibatullah Akhundzada.

"Thank you for sharing such wonderful news. These blessings brought us great joy," James Coleman said in the video. "Such news has also brought us great sorrow. We desperately want to be with our daughter and hold our grandsons, who we long to meet and care for."

He asked the hostage-takers to treat his family like they would treat their own relatives.

"I am asking you to show mercy," James Coleman said. "Please allow Caity and her family to come home."

The letter, described by a source as positive in tone with Caitlan expressing hope about her future, was delivered through a neutral party to the Coleman family.

Caitlan and her Canadian husband, Joshua Boyle, vanished a few days after arriving in Ghazni, Afghanistan, in October 2012 ostensibly as backpacking tourists in the war-torn province near the Pakistan border. She was pregnant at the time and they were believed to have been held in Pakistan, at least initially, by the Afghan Taliban network commanded by the Haqqani family, which exerts influence in Ghazni.

The Haqqani Network has held hostage numerous westerners including U.S. Army Sgt. Bowe Bergdahl and journalists David Rhode and Sean Langan.

Two brief videos from captivity of noticeably thinner Caitlan and Josh -- who was once briefly married to the Palestinian-Canadian daughter of a suspected top al Qaeda financier killed by Pakistani security forces -- were released in June 2014 by their families. It was an effort to raise awareness of their case, in hope that they could establish a line of communication with the captors to negotiate for their release.

It has not been clear whether a ransom for the couple was ever sought by those holding them since there has been no direct communication by them with the Colemans in three and a half years, multiple sources have said.

But James Coleman also made it clear that a large ransom payment would be difficult to raise by their rural family, if a demand is ever made.

Last year, the Obama administration pledged that past U.S. government threats to prosecute hostages' families if they paid terrorists any ransoms -- never enforced, historically, anyway -- would no longer be made.

The new video plea may cause influential Islamic leaders and clerics in the tribal region of Afghanistan and Pakistan to question whether it is legitimate to hold captive a mother and her children against their will, a source familiar with the case told ABC News.

Lynda Coleman expressed joy over the birth of another grandchild.

"What an amazing thing," Lynda Coleman told Circa, regarding the letter believed to have been written by their daughter. "I have two grandsons, she says. I really, really need them home."

Contacted by ABC News today, the Coleman family had no additional comment.