The FBI is now looking into President Biden's Iran envoy, Rob Malley, three sources familiar with the matter told CBS News.

One source familiar with the matter told CBS News that the FBI was looking at Malley's handling of classified material. It is unclear if the bureau's examination encompasses other issues. There was no indication from this source that the FBI considers it a criminal matter at this point.

Congressional intelligence committees are routinely briefed on this type of issue, though lawmakers contacted by CBS News declined to comment, citing the sensitivity of the matter. 

As presidential envoy for Iran, Malley was based at the State Department, and his portfolio included both the attempts to resurrect a nuclear agreement with Iran, as well as negotiations over  at least three American citizens who remain wrongfully detained by Tehran. Malley coordinated closely with both Secretary of State Antony Blinken and the White House National Security Council, whose Middle East division is led by Brett McGurk.

Frustrated by the lack of information sharing with the congressional committees overseeing the State Department, House Foreign Affairs Committee Chair Mike McCaul, Republican of Texas, sent a letter setting a July 11 deadline for the department to provide an update. His letter claimed Congress had been misled about the reason for Malley's absence, which had been attributed to a family health matter.

"We take our oversight obligations extremely seriously," State Department spokesman Matt Miller said Monday. "We obviously got the letter from the chairman; we've been reviewing it and we will be engaging with his office on the matter."

On "Face the Nation," Foreign Relations Committee member Senator Chris Coons, Democrat of Delaware, said he had not been briefed on Malley's "security situation" or on any involvement by the FBI. He, too, called for Congress to be briefed on many Iran-related matters, including the status of any potential negotiation with Iran.

"The Iranians are providing the Russians critical drones and munitions for their aggression in Ukraine," Coons said Sunday. "I think that puts even greater tension on any possible conversations between the United States, our regional allies, and Iran. And I do think we need a briefing to update the members of Congress."

In a statement emailed to CBS News on June 29, Malley said that he was on leave after having been informed that his security clearance is under review. He said then that he had not been provided any further information about what he referred to as an investigation, but said he expects it to be "resolved favorably and soon." He did not specify whether that investigation remained at the Bureau of Diplomatic Security.

In Malley's absence, his deputy is taking over responsibilities. The State Department is not commenting on the matter. 

Miller only reiterated that "Rob Malley is on leave and Abram Paley is leading the Department's work in this area." He added, " In addition to not commenting on any reports of an investigation, I'm really limited about what more I can say about what is a personnel matter due to privacy considerations."

The Department of Justice and FBI also declined to comment.

The FBI's involvement was first reported Friday by Semafor, which referred to the matter as an investigation. 

Pat Milton is a CBS News investigative producer