TRT World's Sally Ayhan has more.
"No response is certainly not appropriate", McConnell said at a Wall Street Journal event.
He added that the USA must send clear and unequivocal message to the Saudis and sanctions beyond what now exist against Riyadh would send that message.
Bob Menendez, the top Democrat on the Senate foreign relations committee, who has called for a strong USA reaction to Khashoggi's death and backs legislation to end all US support for the Saudi coalition waging war in Yemen.
"There is not a smoking gun, there's a smoking saw", Graham, R-South Carolina, told reporters after emerging from a Capitol Hill briefing with Central Intelligence Agency Director Gina Haspel.
"I have zero question in my mind that the crown prince ordered the killing, monitored the killing, knew exactly what was happening", said Bob Corker, a Tennessee Republican. "I think he's complicit in the murder of Mr. Khashoggi to the highest level possible". "There's not a smoking gun but a smoking saw". "It is zero chance - zero - that this happened without the crown prince... you have to be willfully blind" to believe he wasn't involved, Graham said.
"If the crown prince went in front of a jury, he would be convicted in 30 minutes", Corker said.
Some lawmakers were angry Haspel did not participate in a Senate briefing by Trump administration officials last week on Khashoggi's death at the Saudi consulate in Istanbul.
The unusual vote came shortly after a briefing by Mr Trump's Secretary of State, Mike Pompeo, and Secretary of Defence Jim Mattis, who urged senators not to do anything to undermine the US-Saudi relationship.
"If the Saudi government is going to be in the hands of this man for a long time to come, I find it very diffiult to be able to do business because I think he's insane".
Graham also said that he would not support the current US military efforts to support Saudi Arabia in its war against Houthi rebels in Yemen.
The White House official spoke on condition of anonymity because the official wasn't authorised to discuss internal matters publicly.
There were also complains from some senators, wo were not allowed into the briefing. Rand Paul-who asserted that he shouldn't have been excluded from it and that the full Senate should have been briefed rather than strictly a handful of senators.
Graham saying he'd question Pompeo's and Mattis's motives if this were a Democratic administration is a particularly striking statement - and one from someone who is a frequent Trump ally these days. But according to reports, CIA intelligence implicates MBS and indicates that Khashoggi's killers were likely acting on direct orders from the Saudi crown prince. He was killed in what US officials have described as an elaborate plot as he visited the consulate for marriage paperwork.
Prince Mohammed, who has been making his first foreign tour since the October 2 murder of Saudi journalist Jamal Khashoggi, held talks instead with Prime Minister Ahmed Ouyahia, Algeria's presidency said.
The president has touted Saudi arms deals worth billions of dollars to the USA and recently thanked Saudi Arabia for plunging oil prices.