Sen. Ted Cruz is calling for the Pentagon to release an alleged document listing the names of some 500 U.S. service members whose combat deaths can be directly linked to Iran.

Although it's unclear whether such a document exists, the Texas Republican and presidential candidate on Wednesday asked Defense Secretary Ash Carter to release it and notify the fallen service members' families that their deaths were specifically linked to Iran.

"Secretary Carter, I understand that the Joint Personnel Recovery Agency has a classified list of roughly 500 American soldiers who were murdered by Iranian [improvised explosive devices]," Cruz said on Capitol Hill during Carter's testimony.

Carter and other top officials were testifying about the Iranian nuclear deal, which Cruz strongly opposes.

"I would ask Secretary Carter … that the Defense Department release that list to every member of this committee, declassify that list and release it directly to the service members' families who were murdered by General Soleimani," Cruz said, referring to Maj. Gen. Qasem Soleimani, head of Iran's Army of the Guardians of the Islamic Revolutionary Guard.

Carter's response was brief: "Let me look into that and I'll get back to you, senator."

The estimate that 500 U.S. deaths were linked to Iran emerged recently in testimony from Marine Corps Gen. Joseph Dunford, who is President Obama's nominee to be the next chairman of the Joint Chiefs of Staff.

"I know the total number of soldiers, sailors, airmen and Marines that were killed by Iranian activities, and the number has been recently quoted as about 500," Dunford said in his July 9 testimony. "We weren't always able to attribute the casualties we had to Iranian activity, although many times we suspected it was Iranian activity even though we didn't necessarily have the forensics to support that."

A defense official familiar with the estimate told Military Times that the Defense Department does not specifically track casualties linked to Iran and the 500 estimate is a ballpark figure based on intelligence assessments.

But the issue underscores the controversy surrounding Washington's recent nuclear deal with Tehran, a long-sought goal for Obama, but one fiercely opposed by many Republicans in Congress and other critics.

Many of those estimated 500 deaths occurred during the so-called surge in Iraq, when President George W. Bush ordered an influx of tens of thousands of troops to confront what had devolved into a sectarian civil war.

Scores of American personnel were killed or maimed by highly lethal bombs, known as explosively formed penetrators, or EFPs, that Iran manufactured and supplied to Shiite militias across the border in Iraq. Many EFPs were powerful enough to destroy U.S. Humvees and breach tank hulls.

The Iranian-made EFPs first appeared in Iraq in 2005 and for years were the most lethal weapon that American troops faced during the eight-year Iraq war.

Unlike the typical improvised explosive devices U.S. troops encountered there, the EFPs used more sophisticated technology and required more skilled milling to produce. Also known as "shaped" explosives, they used curved copper plates to direct or "shape" the bomb blast.

Some experts believe the estimate of 500 American deaths linked to Iran is probably low. Conducting a detailed forensic analysis on the battlefield and identifying the original source of the IED equipment used is often difficult or impossible.