Even if it is ultimately passed, it can not compel an end to the US intelligence, logistical and diplomatic support for the Saudi campaign.
Speaking to reporters after the briefing, Mattis said he has personally read all the intelligence reports and transcripts related to the killing, which took place October 2 at the Saudi consulate in Istanbul, Turkey.
"There is no direct reporting connecting the crown prince to the order to murder Jamal Khashoggi", Pompeo told reporters.
He said Khashoggi murder "has heightened the Capitol Hill caterwauling and media pile-on".
The Senate on Wednesday advanced a resolution that would end US 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.
Both officials sought to persuade USA lawmakers to maintain US' increasingly contentious backing of Saudi Arabia in the war in Yemen, arguing that pulling back would worsen the brutal conflict.
The gulf between the White House and USA lawmakers regarding Saudi Arabia grew Wednesday after two top members of President Donald Trump's national security team provided a classified briefing to the full Senate.
"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" on a range of issues vital to Mideast stability and Israel's security, Mattis said. Western intelligence agencies, including the CIA, have reportedly concluded that Crown Prince Mohammad bin Salman ordered the murder, while President Trump and other administration officials have cast doubt on that conclusion.
The vote over USA support for the war in Yemen has become a proxy for the Khashoggi murder, with many senators seeing it as a way to punish the Saudis, which the Trump administration has done little to do - a weak response that needs to be balanced, according to Sen.
"I'm talking about any key vote", the South Carolina Republican said.
"We have a problem here".
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Trump told The Washington Post on Tuesday that "maybe I won´t have the meeting". He declined to say what other US officials will join Trump in the session.
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New Jersey Sen. Bob Menendez, the top Democrat on the Senate Foreign Relations Committee, speculated that Haspel didn't attend because she "would have said with a high degree of confidence that the crown prince of Saudi Arabia was involved in the murder of Jamal Khashoggi".
"We also have a crown prince that's out of control, a blockade in Qatar, the arrest of a prime minister in Lebanon, the killing of a journalist", Sen.
The BBC's Barbara Plett Usher in Washington says opposition to the war in Yemen has gained momentum because of outrage at the administration's response to the killing and many in Congress want a tougher stance from the White House. "I think 80 per cent of the people left the hearing this morning not feeling like an appropriate response has been forthcoming", Corker said.
The US Senate on Wednesday subsequently voted 63-37 to advance a resolution to end support for Saudi Arabia's war in Yemen. Bob Corker, a Tennessee Republican and the outgoing chairman of the Senate Foreign Relations Committee.
"The United States can no longer turn a blind eye to this conflict because we are a party to it".
At the heart of the showdown between Congress and the White House is whether the crown prince ordered Khashoggi's killing, with both Republican and Democratic senators saying for weeks that all US intelligence indicates he did, while Trump cast doubt on that and issued unwavering support for the Saudis in an extraordinary statement last week. "And of course Saudi Arabia is absolutely crucial for that goal, and I'm ready to discuss it with the crown prince or with any other Saudi officials because I believe it is a very important objective at the present moment", Guterres told reporters.
Those comments further angered members of Congress who have demanded an investigation of potential involvement by the crown prince.
Several senators complained about the absence of CIA Director Gina Haspel from the closed-door session.
When asked if he had told Trump as much, Graham said, "I just did".
Saudi Arabia began bombing Yemen in March 2015, which was followed by a ground invasion, in the name of restoring the pro-Riyadh regime of President Abdrabbuh Mansur Hadi who was overthrown by Houthi rebels in September 2014. Additionally, Britain has been campaigning in the United Nations for a humanitarian cease-fire and the resumption of food and medical supplies to Yemen.
"Pulling back our limited U.S. military support, our weapons sales to our partners, and our protection of the Saudi and Emirati populations would be misguided on the eve of the promising initial negotiations", he added.