Graham spoke after senators were briefed by Secretary of State Mike Pompeo and Defense Secretary Jim Mattis.
In a rare rebuke of the White House, even Republicans complained they weren't getting the full story. Sen.
The complaints started with the personnel involved.
Mattis, who was joined by Secretary of State Mike Pompeo at the private session, said in remarks released by the Defense Department that overall US national security interests must take precedence over Saudi culpability for the murder of Khashoggi, a Washington Post contributor who disappeared after visiting the Saudi consulate in Istanbul last month.
Trump, who will also attend the summit, will meet Putin as well.
Haspel traveled to Turkey as part of the information-gathering process and is said to have heard an audio recording that depicts Khashoggi's death.
Trump has dismissed the CIA's assessment as inconclusive "feelings" - prompting backlash from the Republicans' most senior ranks.
"So the question for me is whether or not the Central Intelligence Agency supports the conclusion with a high degree of confidence that the crown prince was complicit in the murder of Mr. Khashoggi", Graham told reporters.
"I'm talking about any key vote", Graham said.
Speaking to reporters, Pompeo said there was no direct evidence connecting Saudi Crown Prince Mohammed bin Salman to the Khashoggi killing.
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Several GOP senators, including Lindsey Graham of SC and Rand Paul of Kentucky, have publicly questioned Trump's handling of the situation.
"I don't think there's anybody in that room that doesn't believe he was responsible for it", said Sen. "We understand that Saudi Arabia is an ally, of sorts, and a semi-important country", said Corker, chairman of the Senate Foreign Relations Committee.
The procedural vote received more Republican support than had been expected after a similar resolution fell six votes short of passage earlier this year.
"Anything you need me for, to get out of town, I ain't doing it", Graham threatened.
Senator Cory Gardner, R, said "it would be nice" had Haspel been included in the briefing for lawmakers.
WASHINGTON ― More than 60 senators voted Wednesday afternoon to move forward a bill ending USA support for a Saudi-led coalition fighting in Yemen, offering the biggest condemnation to date of a three-year policy linked to tens of thousands of deaths, hundreds of alleged war crimes and bitter stateside debate under two presidents.
The resolution needs a simple majority to advance in a vote scheduled for Wednesday afternoon. The U.S.is "right on the cusp" of negotiating a ceasefire in Yemen, and the resolution in question would "undermine" that and "encourage the Iranians".
Pompeo said it would be "misguided" to pull back what he characterised as limited USA military support and weapons sales to the Saudis on the eve of potentially promising peace negotiations led by the United Nations.
Western nations are also calling for an end to the Saudi-led military campaign in neighboring Yemen, which was launched by Prince Mohammed, as a humanitarian crisis there worsens. Pompeo said in a strongly-worded op-ed published Wednesday in the Wall Street Journal.
But senators were in no mood to back down. Bernie Sanders, I-Vt., and Mike Lee, R-Utah, fell just six votes short of passage.
Mattis said he had read all the US intelligence reports about the incident and a transcript of what is believed to be an audio recording of the killing.