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 the release 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 in the operations asserted to CNN this week that at least six soldiers were killed in the search for Bergdahl.

The six soldiers at the center of the Bergdahl debate

How did 6 die after Bowe Bergdahl's disappearance?

Also making claims of troop deaths in the Bergdahl search is Sondra Andrews, the mother of 2nd Lt. Darryn Andrews, who was killed in September 2009.

She endorsed accusations by former unit members that Bergdahl deserted and caused U.S. troops to die in the search for him -- though Defense Secretary Chuck Hagel has said it's "unfair" to Bergdahl and his family to presume anything about his disappearance.

Andrews said she believes her son and other troops "were strictly on a mission looking for Bergdahl."

That information is "based on the men that served with Darryn," she told Smerconish.

Andrews said that military should give her family information "on what Darryn was doing and why they lied to us."

"I'd like to see Bergdahl given an opportunity to tell his story, be on trial, have the witnesses come forward and tell their story and get the truth through that, and then I would like to see the full measure of the law followed for his punishment," Andrews said.

Watch: Obama defends Bergdahl swap

Bergdahl went missing on June 30, 2009, in Afghanistan's Paktika province, where he was deployed with the 1st Battalion, 501st Infantry Regiment, 4th Brigade Combat Team, 25th Infantry Division.

An Army fact-finding investigation conducted in the months after his disappearance concluded that Bergdahl left his outpost deliberately and of his own free will, according to the official, who was briefed on the report.

The Army has no definitive finding that Bergdahl deserted because that would require knowing his intent -- something Army officials couldn't learn without talking to the soldier, a U.S. military official told CNN.

See Jake Tapper's special on Bergdahl's time in captivity, life before the Army and what happened the night he disappeared

The Bergdahl Files: A custom magazine

Ed Lavandera and Devon Sayers reported from Hailey, Idaho, and Azadeh Ansari reported and wrote from Atlanta; CNN's Chelsea J. Carter and Michael Martinez contributed to this report.