Speaking in an Oval Office meeting with Reuters, Mr Trump refused to comment on whether Mohammed bin Salman was complicit in the murder, but he provided perhaps his most explicit show of support for the Prince since Khashoggi's death more than two months ago.
Pompeo repeated his assertion that there was no direct evidence linking Crown Prince Mohammed bin Salman to the October 2 murder of Khashoggi in the Saudi consulate in Istanbul, Turkey, despite a Central Intelligence Agency assessment it was likely he ordered the killing.
It appears unlikely that the House would be willing to consider either measure. He said direct evidence linking the crown prince to the killing "isn't yet available".
Aides to Republican House Speaker Paul Ryan did not immediately respond to a request for comment on whether the House planned to vote on the measure if it passed the Senate.
Central Intelligence Agency Director Gina Haspel briefed leaders of the House of Representatives behind closed doors about the killing.
Corker said late Tuesday he would hold off on offering his plan to assuage Democratic concerns that it could be used as a way to peel off support for the Yemen resolution.
Trump told Reuters in an interview on Tuesday that Saudi Crown Prince Mohammed bin Salman "is very strong in power", and standing by the kingdom "certainly" meant standing by the crown prince at this moment.
The Senate voted 60-39 to begin debate on the resolution, S.J.Res. 54.
"If we don't get it through this year we're definitely coming back at it", Menendez said.More news: Kendrick Lamar Received The Most 2019 Grammy Nominations
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The journalist, who had lived in the US and wrote for The Washington Post, had been critical of the Saudi regime.
However, he added that he could abide by legislation that requires to end US support for the Saudi-led attack in Yemen, noting that "I'm much more open to Yemen because frankly, I hate to see what's going on in Yemen".
The United States imposed economic sanctions on 17 Saudi officials last month for their role in the killing, stopping short of action that might affect lucrative USA arms deals with Saudi Arabia that Trump has vowed to preserve.
After few weeks, Riyadh accepted the fact that the group of 15 Saudi "rogue" agents killed Khashoggi, leading to an worldwide furore and complicating the already delicate relations between Saudi Arabia, Turkey, and the US. "This is a developing set of facts with respect to the murder of Jamal Khashoggi", he said.
After initially saying he had left the consulate alive, weeks later the Saudi Arabia admitted he was killed there.
"Our expectation is actually for none of this to be necessary and for Saudi Arabia to cooperate for those responsible to be found out", he said.
House Democrats are also expected to keep the issue alive when they take the majority in January.
According to a separate report of NBC News on Tuesday, CIA Director Gina Haspel will brief the House leaders on Wednesday about what USA intelligence community knows about the murder of Khashoggi.
A rapprochement with Saudi Arabia in particular, a regional heavyweight and rival of Iran, would be a considerable breakthrough for Israel.