The Senate voted 63-37 to agree to a motion to discharge the Foreign Relations Committee from considering the measure, which authorizes the chamber to begin mulling the resolution, a debate that is likely to occur next week.
"The bottom line is the United States should not be supporting a catastrophic war led by a despotic regime with a risky and irresponsible military policy", Sanders said in a statement after Wednesday's vote.
But at least five of the Republican Senators who voted against the bill have received funding from lobbyists working for Saudi Arabia, a fact that illustrates how the Kingdom uses its vast wealth to influence US foreign policy.
The bill, which would end USA military support for the Saudi-led campaign in Yemen, passed by a vote of 63-to-37 on Wednesday. The U.S., Germany and France have already done something similar.
Mattis, in prepared remarks released by the Pentagon, said told senators that morning that cutting off US military support would undercut diplomatic efforts to end Yemen's civil war.
"Our security interests can not be dismissed", Mattis said, even as Washington seeks accountability for Khashoggi's murder, a crime which "our country does not condone".
"We are seldom free to work with unblemished partners", Mattis told senators.
Senator Murphy, however, said Pompeo and Mattis' testimony may have been counterproductive. "Saudi Arabia, due to geography and the Iranian threat, is fundamental to maintaining regional and Israeli security, and to our interest in Mid-East stability".
Mattis and Pompeo worry a move to cut U.S. support to the Saudis ahead of the summit is poorly timed and could embolden Huthis not to negotiate.
While Mattis was sober, Pompeo struck an antagonistic tone in an op-ed published by the Wall Street Journal on the morning of the briefing.
Seems to counter recent statements by both the US Ambassador to the UN Nikki Haley and senior White House officials including Mattis and Pompeo, who last month called for the cease-fire.
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Germany has halted arms sales to Saudi Arabia in response to the killing and urged others to do the same.
CIA Director Gina Haspel didn't attend a Senate briefing on the murder of Jamal Khashoggi and the Saudi war in Yemen.
Khashoggi, who lived in the US and wrote for The Washington Post, was publicly critical of the Saudi crown prince.
Pompeo told reporters after the briefing that there was "no direct" evidence linking the crown prince to the murder, but senators remained unconvinced and frustrated.
The director of Canada's spy service travelled to Turkey and heard a recording of the Khashoggi's killing during a briefing provided by Turkish officials.
Pointing out that a partnership with Saudi Arabia has its benefits in various fields, Pompeo wrote that Riyadh is a powerful force for stability in the Middle East and contributed millions of dollars to the US -led efforts to fight Daesh in Syria.
"I am not going to blow past this", Republican Senator Lindsey Graham said. He noted that the measure may yet be amended to find some middle ground.
Pompeo criticized those who are using "the Khashoggi murder" for ulterior motives, saying: "Is it any coincidence that the people using the Khashoggi murder as a cudgel against President Trump's Saudi Arabia policy are the same people who supported Barack Obama's rapprochement with Iran - a regime that has killed thousands world-wide, including hundreds of Americans, and brutalizes its own people?"
The public prosecutor says 18 Saudi nationals have been detained.
Senate Foreign Relations Committee ranking member Bob Menendez, D-N.J., accused the administration of a "coverup" in Khashoggi's murder because Haspel was not made available. Senator Sanders first introduced this bill in February of this year, and unfortunately it was tabled in March, so they voted not to vote on the bill back in March.
The vote is a sign of increasing frustration with Trump's unwillingness to hold Saudi Arabia accountable for the murder of Washington Post contributor Jamal Khashoggi, a critic of Saudi Crown Prince Mohammed bin Salman, who was assassinated by Saudi agents while visiting the Saudi consulate in Istanbul in October.