Editor's note: Read a version of this story in Arabic.

Hailey, Idaho (CNN) -- The FBI is investigating threats against the parents of Army Sgt. Bowe Bergdahl, the latest development in a case that has put the spotlight on the circumstances surrounding his capture in Afghanistan and release by the Taliban.

"We are working jointly with our state and local partners and taking each threat seriously," FBI Special Agent William Facer told CNN in an e-mail on Saturday.

Facer declined to detail the nature and severity of the threats, and a military spokesperson for the Bergdahls declined to comment.

Bergdahl's parents have not been seen publicly since the announcement last week that the soldier had been freed from five years in captivity at the hands of the Taliban in exchange for therelease of five detainees at Guantanamo Bay Naval Base.

Bergdahl's release raises questions

The news comes as a fallen soldier's mother and a former member of Bergdahl's unit continued to assert that troops were killed while searching for the soldier in eastern Afghanistan.

Pentagon and Army officials have looked at such claims, and "right now there is no evidence to back that up," a U.S. official, speaking on condition of anonymity, has told CNN.

But former Sgt. Matt Vierkant, a member of Bergdahl's platoon, told CNN's Michael Smerconish that "men were injured and killed in the search for him."

"The mission was to find Bergdahl," Vierkant said.

In the week since Bergdahl was released by the Taliban, a controversy has grown over whether troops were killed, directly or indirectly, in the search.

Former soldiers involved