(CNN) Senate Foreign Relations Chairman Bob Corker said Thursday he was working with senators from both parties to try to cut a deal to formally rebuke Saudi Arabia over its role in the murder of journalist Jamal Khashoggi, the latest sign that Republicans want to go further than President Donald Trump in responding to the actions of a key US ally.

Corker's announcement came hours after Republican Sen. Lindsey Graham said that the CIA has now agreed to brief him on Khashoggi, following outrage from both sides of the aisle that Wednesday's Saudi and Yemen briefing on Capitol Hill did not include the Central Intelligence Agency.

Corker, a Tennessee Republican who's retiring at the end of his term in January, told CNN his hope is to reach a broad bipartisan deal that will piece together various senators' proposals taking aim at the Saudi kingdom. Then, he said, he hopes to use the new deal as a substitute for a resolution moving through the Senate that would end US involvement in the Saudi-led war in Yemen.

"We are working on an amendment that would strike what's on the floor and more fully express ourselves as to what our policy should be towards Saudi Arabia," Corker said.

Exactly what that language entails -- and whether it would seek to end the US role in Yemen or seek to impose sanctions on the Saudi crown prince Mohammed bin Salman -- remains to be seen.

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