The chairman of the Senate Foreign Relations Committee said Wednesday that the Trump administration is not opposed to Congress pursuing a new war authorization, following a classified briefing with the defense secretary and secretary of state.

Defense Secretary Jim Mattis and Secretary of State Rex Tillerson briefed Sen. Bob Corker, R-Tenn., and his committee for hours behind closed doors. The committee is considering replacing the 9/11-era authorization for the use of force, or AUMF, that the Trump administration and the two previous administrations have used as a legal justification for waging wars against al-Qaeda and the Islamic State.

"They wouldn't be opposed to one that was written in the appropriate way but actually [Defense Secretary Jim] Mattis was very helpful in talking through some of the caveats they might want to put in place," said Sen. Bob Corker, R-Tenn.

Because the briefing was classified, Corker and other senators declined to discuss what requests Mattis and Tillerson made about the details of any future AUMF.

Just before the hearing, the State Department sent a letter to Corker Wednesday claiming the administration has the legal authority it needs to fight wars against the terrorist group around the world and is not looking for revisions to the existing AUMF. But Corker said he doesn't think that closes the door on a new AUMF.

"I'm confident they will work with us," Corker said. "They are not seeking one but I think they saw that there's an effort to try to do something with it."

Sen. Tim Kaine, D-Va., who is sponsoring legislation to replace the existing AUMF, said Mattis repeated recent public testimony that he made to Congress, saying during the classified briefing that he believes passing a new war authorization would send a message of support to U.S. troops.

"They were very open to the idea of working on an authorization, not because they feel like they legally have to have it, but they think for the mission itself it would be good to have Congress engaged in that way," he said. "They would not want an authorization to put restrictions that would be either tactically unwise or would tread over into Article II territory."

Kaine was referring to the section of the Constitution that lays out the president's powers as commander-in-chief of the military.

Still, committee members appeared divided on how to proceed after leaving the briefing.

Kaine said there is "significant difference of opinion" on the committee as to whether the Trump administration does indeed have the legal authority for all ongoing military operations, such as strikes on President Bashar Assad's forces in Syria.

His bill, cosponsored by Sen. Jeff Flake, R-Ariz., would create a new AUMF that defines the specific groups the U.S. is fighting, gives Congress discretion over where military operations are waged, and requires an update after five years.

Corker said he was unsure whether there was a need for any hearings on the issue.

Sen. Ben Cardin, D-Md., the ranking Foreign Affairs member, said after the briefing he will continue to push for a new war authorization that repeals the 2001 AUMF and imposes future review and renewal by lawmakers.

"My own views have not changed," Cardin said. "I think it is important for Congress to take up an AUMF, that the 2001 AUMF was never intended to cover military operations against ISIS."