Among the options: pull back from United States involvement in the Saudi-led war in Yemen; deny any arms sales with Saudi Arabia; slap the crown prince with sanctions, along with a resolution saying the Senate finds him complicit in murder.
Mr Khashoggi entered the Saudi consulate in Istanbul on October 2, and inside was tortured, drugged and dismembered before being disposed of.
Saudi authorities have previously said the agents who killed Khashoggi exceeded their authority.
"There is not a smoking gun, there's a smoking saw", Graham said.
Turkish President Recep Tayyip Erdogan said the order to kill came from the highest levels of the Saudi regime while insisting it was not from King Salman.
"If someone is saying that Secretary Mattis or Secretary Pompeo were dishonest, they just don't know those individuals", Stewart said.
At last week's hearing, Secretary of State Mike Pompeo and Defence Secretary James Mattis told senators there was no direct evidence of the crown prince's involvement in Khashoggi's death.
"I think the secretary of Defense and secretary of State are in a bad spot because the president has given this bear hug to MBS and to the entire Saudi regime, so they are bound to carry out his freakish policy", he told MSNBC. He was not in Haspel's briefing, which was attended by a select number of committee chairs and top-ranking Democrats. It's among several measures being considered after a closed Central Intelligence Agency briefing on Capitol Hill.
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President Trump has equivocated about assigning blame for Khashoggi's killing, frustrating lawmakers from both parties.
Instead, he said, he would rally support for a different, broader effort against the kingdom - to cut off arms sales and military aid for the war in Yemen, and impose new sanctions on those responsible for the killing, including the crown prince. Todd Young (R) said the administration was "clearly and directly blown off" by Riyadh. "There are all sorts of things we can do to make clear this can't continue to happen". As the leader of the free world, we have to accomplish two goals: defend human rights while also attempting to maintain important relationships with key allies that we hope will help us bring stability to critical parts of the world.
Saudi Arabia has so far detained 21 people in connection and is seeking death penalties against five of them.
The U.S. has slapped sanctions on Saudis involved in the murder.
Blunt told reporters at the time that the House was unlikley to move on the resolution, and he didn't think a Senate debate on Yemen would be particularly helpful in encouraging the peace process along.
Corker has said he expects votes on amendments to the Yemen war powers resolution on Monday. Though it was passed almost 50 years ago, there is still a debate over whether the resolution is constitutional. "Guilty. A guilty verdict", Corker, the chairman of the Senate Foreign Relations Committee, told reporters after the briefing.
Graham is one of the sponsors of the non-binding resolution.
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