Story highlights Top Trump officials are briefing a Senate panel on a new ISIS war authorization

Congress has been unwilling and unable to pass an authorization for the ISIS war

(CNN) Defense Secretary James Mattis and Secretary of State Rex Tillerson don't need a new war authorization to fight ISIS, they told Congress on Wednesday. But if Congress wants to pass one, then they'd be happy to support it.

Mattis and Tillerson discussed the prospects for a new war authorization behind closed doors with the Senate Foreign Relations Committee, where lawmakers said they had a productive discussion but aren't necessarily closer to resolving the prickly issues that have kept Congress from passing an Authorization for Use of Military Force (AUMF) since the US began fighting ISIS in 2014.

Sen. Tim Kaine, who has led the push in the Senate to vote on the ISIS war, said he was encouraged by the discussion with Mattis and Tillerson.

"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," the Virginia Democrat told reporters after leaving the classified setting.

But the Trump administration made clear ahead of Wednesday's briefing that the military did have the legal authority it needed. The State Department sent Senate Foreign Relations Chairman Bob Corker a letter Wednesday stating the US "has sufficient legal authority to prosecute the campaign against al Qaeda and associated forces, including against the Islamic State."

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