Sen. John McCain, R-Ariz., is demanding to know why a suspected ISIS member, who allegedly was "complicit" in the capture of American hostage Kayla Mueller, was handed over to Kurdish authorities instead of being extradited to the U.S. for trial.

Nasrin As’ad Ibrahim, commonly known as Umm Sayyaf, was caught on May 15 during an operation by U.S. forces that killed her husband, Abu Sayyaf – a key Islamic State leader in charge of the group’s oil and gas operations in eastern Syria – along with 11 other jihadists.

The Pentagon announced the transfer of Umm Sayyaf to Kurdish custody in Iraq last week. The White House, though, has claimed she was complicit in the August 2013 capture of Mueller, an Arizona aid worker in Syria who was later killed. ISIS claimed in February that Mueller died in a Jordanian airstrike, a claim the Pentagon has rejected; the U.S. has not been able to confirm the precise cause of her death or the timing. 

McCain, in a letter dated Aug. 13 and sent to Defense Secretary Ashton Carter and Attorney General Loretta Lynch, asked why Sayyaf was not extradited considering she “was clearly involved at the top levels of a foreign terrorist organization with which the United States is in a state of hostilities.”

“In light of those circumstances, I would respectfully request a detailed explanation in writing for why Umm Sayyaf was not extradited to the United States to stand trial,” the chairman of the Senate Armed Services Committee wrote. 

A McCain spokesperson told FoxNews.com that McCain has a connection to the case as Mueller was from Prescott, Ariz., and McCain was active in efforts to try to locate her before she was killed. McCain also spoke at her memorial service in Prescott earlier this year.

McCain asked whether DOJ representatives recommended bringing charges against Sayyaf in the U.S. prior to her release.

“I would also like to know what commitments, if any, the Kurdistan Regional Government or the Government of Iraq have provided to ensure that Umm Sayyaf is held responsible for her actions,” McCain wrote. 

The Wall Street Journal reported last week that U.S. officials had in fact mulled extraditing Sayyaf to the U.S. but Iraqi officials resisted, citing a constitutional ban on surrendering citizens to foreign authorities. 

As a result, the U.S. reportedly decided to turn her over to Kurdish authorities. 

White House Press Secretary Josh Earnest also told reporters last Friday that U.S. personnel had the opportunity to interrogate Sayyaf “for an extended period of time.”

Earnest said the transfer determination was “conducted in full coordination with the government of Iraq, and both the United States and the Iraqi government are fully supportive of this transfer.”

“We have a firm belief that in the context of the Iraqi criminal justice system that she will be held to account for her crimes,” Earnest said. 

A Department of Defense spokesman told FoxNews.com they have not yet responded to the McCain letter. “Whenever we receive a letter like this from congressional staff, we will always respond promptly and directly, and we certainly appreciate his concerns,” the spokesman said.

A DOJ spokesman said: "We are aware of the letter and will respond at the appropriate time."

Fox News' Matt Dean contributed to this report.

Adam Shaw is a Politics Reporter and occasional Opinion writer for FoxNews.com. He can be reached here or on Twitter: @AdamShawNY.