The Senate on Wednesday advanced a resolution that would end U.S. military support for the Saudi-led conflict in Yemen that human rights advocates say is wreaking havoc on the country and subjecting civilians to indiscriminate bombing.

The procedural vote was 63-37, a rebuke to Saudi Arabia and President Trump's administration, which has issued a veto threat. Late Wednesday, the Senate agreed to postpone any further action on the resolution until next week.

Lawmakers from both parties have signaled they want to punish Saudi Arabia for its role in the murder of writer and activist Jamal Khashoggi.

The U.S. is not directly involved in the civil war, but provides assistance to the Saudi-led coalition, including intelligence sharing and weapons sales. There has been increased scrutiny of that support in the wake of the killing of Khashoggi at a Saudi consulate in Turkey. U.S. intelligence agencies are said to have concluded that Saudi Crown Prince Mohammad bin Salman must have at least known about the plan to kill Khashoggi, although Trump has appeared to doubt that assessment.

After a closed-door briefing with Secretary of State Mike Pompeo and Defense Secretary James Mattis, as Fox News previously reported, several senators said they were unsatisfied and likely to back the resolution to halt U.S. interference.

Sen. Lindsey Graham, R-S.C., told Fox News after the vote: “I changed my mind ’cause I’m pi--ed. … I don’t agree with what they’re doing. The way the administration has handled Saudi has been unacceptable, briefing didn’t help me today at all. Yemen is just one part of the puzzle. I think we have a right to be briefed by the CIA. How can I make an informed decision if I don’t have access to intelligence?”

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Emerging from the briefing, Pompeo said the vote would be "poorly timed" as diplomatic efforts to end the conflict are underway.

The years-long war, which began after the Houthis ousted the Yemen government in 2014, has wreaked havoc upon the country, and led to the bombing of civilians and a devastating cholera outbreak.

Tens of thousands of people are believed to have been killed in the conflict. Two-thirds of Yemen’s 27 million population rely on aid and more than 8 million are at risk of starvation. U.N. Special Envoy Martin Griffiths told the U.N. Security Council this month that Yemen “remains the largest humanitarian disaster in the world,” and civilians are dying from preventable diseases as the economy remains on the verge of collapse.

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“The United States can no longer turn a blind eye to this conflict because we are a party to it. The longer we enable the conflict to continue, the more innocent men, women and children will die,” said Sen. Dianne Feinstein, D-Calif., in a statement to Fox News after the vote. “I welcomed Secretary Mattis’ announcement that the United States will no longer refuel the coalition’s aircraft. But more must be done. Until there is a congressional authorization, all U.S. forces supporting the coalition’s war should be withdrawn. That’s why I support the Sanders-Lee resolution. By ending our participation in this brutal war, we will send an unambiguous message that we won’t accept continued bloodshed.”

Fox News’ Chad Pergram, Kristina Biddle, Adam Shaw and The Associated Press contributed to this report.