But Secretary of State Rex Tillerson and Secretary of Defense James Mattis also insisted in a closed-door hearing that the administration believes it needs no new legal authority to conduct its military operations in the region.
"The administration is not seeking" a new AUMF, but "they wouldn't be opposed to one that was written in the appropriate way" and did not leave a gap after the original authorization was repealed, Senate Foreign Relations Committee Chairman Bob Corker told reporters after the hearing.
The pair said "they'd be very open" to replacing existing authorization with new language, he added.
The legislation -- and its passage by Congress and approval by the president -- could still be months away.
If approved, it would be the first significant update to the authorization passed as a response to the 9/11 attacks of 2001.
Corker said he was "confident" that the administration would work with Congress on the issue.
Several US lawmakers from both parties have warned that using the 2001 authorization to engage in new conflicts is a blank check for war.
It has been used to justify the Iraq War, and operations against the Islamic State extremist group.
'Unbridgeable' differences
Democratic Senator Tim Kaine, who has been working with Republican Jeff Flake on a new, tailored AUMF, said Mattis conceded that while no new authorization was legally required, it could be good policy.
Kaine, citing Mattis's testimony, said that "if you do an authorization now, you express a congressional resolve, which is really the American public's resolve, and send a message to our allies, you send a message to our adversaries, you send a message of support to our troops."
The Kaine-Flake AUMF would expand the authority to combat not just the Taliban, but the Islamic State and Al-Qaeda. It would also delineate the authority's geographic area and duration.
The Trump administration, like Barack Obama's administration before it, argues that US forces are legally prosecuting the fight against ISIS and Al-Qaeda in Syria and Iraq under the previous AUMF.
Senate Democrat Chris Murphy said differences between the administration's position and several lawmakers were "unbridgeable."
But he expressed optimism that Tillerson and Mattis "clearly were willing to work on an AUMF."
In June, a House committee approved an amendment in a broader defense spending bill that would end the 2001 AUMF within eight months.
Republican leadership stripped the measure out of the final bill before passage.
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