US Senator Bob Corker, the current head of the Senate Committee on Foreign Relations, also said after the meeting that there was no doubt in his mind that MBS ordered Khashoggi's murder.
He noted that there have been reports that the Central Intelligence Agency has concluded that Saudi Crown Prince Mohammed bin Salman was complicit in Khashoggi's murder, but he has not been allowed to see what evidence - direct or indirect - led to that conclusion.
"It could very well be that the crown prince had knowledge of this tragic event - maybe he did and maybe he didn't!"
"There is not a smoking gun, there is a smoking saw", Republican Senator Lindsay Graham told reporters, also after the briefing.
The source said the briefing will include leaders of the Senate Foreign Relations Committee, Armed Services Committee and Appropriations Committee. "I think he is unsafe, and he has put the relationship at risk".
"I think the behaviour before the Khashoggi murder was beyond disturbing and I can not see him being a reliable partner to the United States".
Khashoggi, a former Washington Post columnist and Saudi dissident, went missing October 2 following what was supposed to be a routine stop at the Saudi consulate in Istanbul. President Donald Trump has equivocated over who is to blame.
Sen. Bob Corker says a jury would find the Saudi crown prince 'in about 30 minutes.'
The Senate is due to vote in the coming days on a measure that would cut off United States military support for Saudi military operations in Yemen.
Turkish investigators allege Khashoggi was tortured before he was murdered by Saudi officials in the country's consulate in Istanbul.
Soon after that briefing, led by Secretary of State Mike Pompeo and Secretary of Defense James Mattis, senators voted overwhelmingly to advance a resolution to cut American military assistance to Saudi Arabia.
"It's wrong for the Central Intelligence Agency to have expressed a conclusion that the crown prince was involved in the killing of Khashoggi and then withhold that information", he told reporters. Rand Paul believes Haspel should share the CIA's findings with all members of Congress.
"Were there text messages sent back from the killers to the crown prince's office?"
Echoing Trump's public comments on the killing, Pompeo said after last week's briefing with senators that there was "no direct reporting" connecting the crown prince to the murder.
Trump's new NAFTA faces uphill battle in Congress
Pelosi, who is expected to take the role of House Speaker in January, has repeatedly expressed deep concerns over the deal's enforceability.