The South Carolina Republican described the Saudi royal as "a wrecking ball", "crazy" and "dangerous".
The Saudis have charged 11 people but deny the crown prince was involved.
"There is not a smoking gun - there is a smoking saw," Graham said, referring to Khashoggi's alleged dismemberment in the Saudi consulate in Istanbul in October.
Senator Bob Menendez, a New Jersey Democrat, echoed those views.
He said the US must "send a clear and unequivocal message that such actions are not acceptable in the world's stage".
Another senator, Bob Corker, told reporters, using the crown prince's initials: "I have zero question on my mind that the crown prince MBS ordered the killing."
The Tennessee Republican added: "If he was in front of a jury, he would be convicted in 30 minutes. Guilty."
The Senate is planning to vote on a proposal to end US military support to the Saudi-led coalition fighting in Yemen, after members of both parties advanced the resolution last week.
Senator Chris Murphy, who was not privy to Tuesday's briefing, criticised the Trump administration.
"Not everything needs to be secret," the Connecticut Democrat tweeted.
"If our government knows that Saudi leaders were involved in the murder of a US resident, why shouldn't the public know this?"
The CIA has concluded Mohammed bin Salman "probably ordered" the killing of Khashoggi.
The spy agency has evidence he exchanged messages with Saud al-Qahtani, who allegedly oversaw the Saudi reporter's murder.
The CIA director -- who has reportedly heard an audio recording of the murder -- did not attend a recent congressional briefing by cabinet members, dismaying lawmakers.
The White House denied having a hand in Ms Haspel's conspicuous absence, and the CIA said no one had told Haspel not to attend.
Trump has said the CIA findings on the crown prince were not conclusive.
On November 20, he said: "It could very well be that the crown prince had knowledge of this tragic event - maybe he did and maybe he didn't."
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)