Saudi Arabia has so far detained 21 people in connection and is seeking death penalties against five of them. Assiri and Qahtani were reportedly suspended from their duties but they do not face criminal charges.
But it emphasized that it would "continue as before to welcome scholars and students from Saudi Arabia to the Harvard community".
"If there is going to be some coordinated action to send a strong signal, we should do so in the next two to three weeks before there is a break that will, I think, dissipate some of the focus and energy [regarding Saudi Arabia]", Democrat Chris Coons of DE told VOA.
"It'll have teeth", said Senate Foreign Relations Committee Chairman Bob Corker, a Tennessee Republican, who added that the senators are trying to piece together various proposals into one plan to achieve bipartisan consensus.
He also said: "There's not a smoking gun, there's a smoking saw".
Bin Salman has denied any knowledge of the plot to torture, murder and dismember Khashoggi at the Saudi Consulate in Turkey in October and the USA has waffled on whether it believes his denials.
Senators in both parties have been enraged over the killing and over Trump's equivocating on who is to blame. But the Senate could vote to end that arms sale or end United States support of Saudi Arabia's war in Yemen.
Trump's China auto tariffs claim sows confusion
The uncertainty underscored the risk entailed by Trump's eagerness to strike deals without nailing down details in advance. Trump also threatened to impose tariffs on the remaining $267 billion worth of Chinese goods not now subject to tariffs.
Last week, the administration sent Secretary of State Mike Pompeo and Defense Secretary James Mattis to brief the Senate, but Graham and other senators expressed outrage that they were not hearing directly from Haspel, as the CIA's assessment had been liberally leaked to the media.
"Better answers" are needed from Saudi Arabia on the killing of journalist Jamal Khashoggi, says Prime Minister Justin Trudeau. Human rights groups say the war is wreaking havoc on the country and subjecting civilians to indiscriminate bombing.
USA intelligence officials have concluded that the crown prince must have at least known of the plot, but Trump has been reluctant to pin the blame. Richard Shelby (R-Ala.) said, "All evidence points to that, that all this leads back to the crown prince".
Murphy noted that the debate would have to kick over into next year regardless of whether the Senate passes the resolution, as House Republicans are unlikely to approve it while they remain in the majority before January.
Mattis and Pompeo have defended the strategic relationship and downplayed the crown prince's ties to the murder. He was not in Haspel's briefing, which was attended by a select number of committee chairs and top-ranking Democrats. "It's not based on friendship as much as it's based on common interests, combating extremism in the Middle East and countering the Iranian threat", said Senator John Cornyn, the chamber's No. 2 Republican.
"I think we have lost a lot of our moral high ground", McCaskill said on the day of the vote.