Washington (CNN) US senators have rebuked the Trump administration after being denied a CIA briefing on the killing of journalist Jamal Khashoggi , voting to consider cutting US military support to the Saudis in the war in Yemen.

Senators from both parties -- including one of President Donald Trump's most vocal allies, South Carolina Republican Sen. Lindsey Graham -- seemed furious after a closed-door briefing with Secretary of State Mike Pompeo, who defended the administration's response to Khashoggi's murder, saying after the briefing there was "no direct reporting" that connected Saudi Crown Prince Mohammad bin Salman to the killing.

Amid lingering frustrations, lawmakers voted 63-37 to advance a resolution opposed by the administration to cut US support to the Saudis in Yemen.

Pompeo and Defense Secretary James Mattis traveled to Capitol Hill for a briefing with Senate lawmakers on Yemen where they emphasized the strategic importance of the US-Saudi relationship and defended the administration's response to Khashoggi's murder. But the session appears to have backfired.

The purpose of Wednesday's briefing was to outline the US role in Yemen -- a briefing that has taken on added importance as momentum has grown behind a resolution to cut off US military aid to Saudi Arabia over its role in the brutal civil war in the country.

At least in part, the briefing was designed to push back against the resolution, which the Trump administration opposes.

But hours after the session, the Senate voted to advance the resolution -- which was co-sponsored by Independent Sen. Bernie Sanders from Vermont, Republican Sen. Mike Lee from Utah and others -- ending US support for the Saudi-led war in Yemen out of committee.

While the bill may still be reshaped by amendments or input from the administration, the vote illustrates the level of congressional discontent over Wednesday's hearing.

Graham, who said he was not satisfied by Pompeo and Mattis' testimony, told reporters that he switched his vote on the Yemen resolution because he's "pissed."

"I changed my mind because I'm pissed," Graham said. He continued to blast the administration's handling of the Khashoggi situation. "The way the administration has handled it is not acceptable."

He said he spoke to the White House Wednesday about his concerns. "I said, listen, it's pretty obvious to me that we're a co-equal branch, you've made your assessments about what the intelligence shows, I'd like to make my own. The only way I can make that assessment is to be briefed. If it is credible that the crown prince was complicit, then I will take action consistent with that."

Those actions, he indicated, would include suspending arm sales and support of the war in Yemen.

Lawmakers want answers from CIA

Senators from both parties made clear prior to the briefing that they intended to ask for details on the Khashoggi murder, even as the Trump administration declined to send CIA Director Gina Haspel to join the briefing.

Speaking to reporters after the briefing, Pompeo said there is "no direct reporting" connecting the crown prince to the murder of Khashoggi.

Mattis echoed that point telling reporters "we have no smoking gun that the crown prince was involved" in the killing. Mattis said he read all the intelligence reports and transcripts himself.

But when he was asked if it was true the CIA expressed high confidence, Mattis would only say, "there you need to go to the CIA."

"The administration position was defended by both of them in terms of what we had done naming 17 people who would suffer because we believed they were involved. But there was no satisfying answer about how it is possible that this could have occurred without the crown prince's knowledge or direction," Democrat Sen. Dick Durbin told CNN.

A US official told CNN last week that there is still is no smoking gun implicating the crown prince directly and the intelligence assessment is ongoing. Intelligence officials have said the CIA presented the President with a confidence-based assessment given the facts of the situation.

Though sources tell CNN that the CIA has assessed with high confidence that the prince directed Khashoggi's murder, which was conducted by members of bin Salman's inner circle, the fact that they don't make a final conclusion gives the White House an out.

Haspel found herself at the center of a political dispute Tuesday amid reports that the White House was blocking her from attending the briefing, a claim national security adviser John Bolton denied.

But after Wednesday's briefing, Durbin said lawmakers were told by those present that the decision was made by the White House.

"The absence of Gina Haspel was raised by Democrats and Republicans and we were told by those who were there, it was a decision by the White House she not be present," he said.

Asked if the a reason was given, Durbin said, "no."

Pompeo was also asked by reporters why Haspel was not present for the briefing with senators.

"I was asked to be here and here I am," he said. When pushed on the issue, Pompeo repeated, "I was asked to be here and I am here."

Later Wednesday, the CIA issued a statement pushing back on claims that the White House, or anyone else told Haspel not to attend the briefing.

"While Director Haspel did not attend today's Yemen policy briefing, the Agency has already briefed the Senate Select Committee on Intelligence and Congressional leadership on the totality of the compartmented, classified intelligence and will continue to provide updates on this important matter to policymakers and Congress. The notion that anyone told Director Haspel not to attend today's briefing is false," according to the statement from CIA Press Secretary Timothy Barrett.

Still, Republican Sen. Lindsey Graham made his feelings known, calling the briefing "inadequate, because the CIA was not there" to answer questions and demanding a briefing from the agency.

"I'm not going to be denied," Graham said, adding that if a briefing by the CIA is not done soon, "it's going to be hard for me to vote for any spending bill."

"Anything that you need me for to get out of town, I ain't doing it until we hear from the CIA," he said.

Asked if he has made his position clear to the President, Graham pointed to the cameras and said "I just did."

Briefing backfires

In prepared remarks, both Pompeo and Mattis urged senators not to abandon US involvement in Yemen conflict and defended the importance of Saudi Arabia as a key partner in the region.

"I know many of you think it's time to pack up and abandon the role we've been playing since the previous administration. I'm here to tell you why that's a bad call," Pompeo said.

"The more support from you we get, the better chance we have of ending the conflict and stopping the suffering that none of us are happy about," Pompeo added.

Pompeo laid out what he described as "three vital missions" being carried out by the US: "to assist the Saudis and the Emiratis in their fight against Iranian-backed Houthi fighters," "to decapitate al-Qaeda in the Arabian Peninsula," and "to protect Americans working in Saudi Arabia or transiting the strategic waterways around Yemen."

He also devoted a large portion of his remarks to Iran's malign influence in the region.

Mattis acknowledged Khashoggi's murder in his own prepared comments but said US "security interests cannot be dismissed, even as we seek accountability for what President Trump described as the 'unacceptable and horrible crime' of Jamal Khashoggi's murder, a crime which 'our country does not condone.'"

"We must maintain our twin requirements of holding those responsible for the murder to account, while recognizing the reality of Saudi Arabia as a necessary strategic partner. We cannot be deflected from using all our influence to end this war for the good of innocent people in trouble, and ultimately the safety of our own people, and this includes our military engagement," he said.

While the Yemen resolution has little future in the current GOP-led US House and has already failed once in the Senate this year, Wednesday's vote underscores the growing amount of discontent on Capitol Hill with the administration and US relations with Saudi Arabia, aides said.

Prior to the vote, Pompeo expressed the administration's opposition to the resolution, calling it "poorly timed" and saying it could curtail diplomatic efforts underway aimed at achieving a ceasefire agreement, adding the US is "on the cusp" of getting the parties to the table.

While Pompeo said Iran would not be a direct party to the talks, he hoped Tehran "won't upset the apple cart" through their support of Houthi rebels in Yemen and scuttle the discussions.

But just hours later, lawmakers advanced the resolution by a vote of 63-37.

Support for the resolution, which had previously been rejected, grew during the day as 14 Republicans joined all 49 Democrats in voting to advance the measure.