Senator Bob Menendez, the Foreign Relations Committee's top Democrat, said Washington was basically telling an ally "you can kill with impunity."
"It is outrageous that we are willing to turn our eye away from such a murder because we have 'interests,"' Menendez said.
Trump has dismissed a CIA assessment that the crown prince likely ordered Khashoggi's killing. He vowed last week to remain a "steadfast partner" of Saudi Arabia and said it was not clear whether the prince knew about the plan to kill Khashoggi.
Those comments further angered members of Congress who have demanded an investigation of potential involvement by the crown prince.
Many were angry that CIA Director Gina Haspel did not participate in the briefing, as they had requested.
Republican Senator Lindsey Graham, who has been one of Trump's closest congressional allies, said he wanted to know whether the CIA assessment supports his belief that the killing could not have happened without the prince's knowledge.
Graham said he would withhold his vote on any key issue, including must-pass spending bills, until the CIA briefs senators about Khashoggi's killing.
When asked if he had told Trump as much, Graham said, "I just did."
Saudi Arabia and other Gulf Arab states have been battling in Yemen since 2015 to restore a government driven out by the Houthis, Shi'ite Muslim fighters that Yemen's neighbors view as agents of Iran. The war has killed more than 10,000 people and created the world's most urgent humanitarian emergency.
Pompeo said the United States would provide an additional $131 million for food aid in Yemen.
Mattis said pulling back U.S. military support in Yemen and stopping weapons sales to important partners would be misguided.
"Our security interests cannot be dismissed," Mattis said, even as Washington seeks accountability for Khashoggi's murder, a crime which "our country does not condone."
An Argentine federal judge reviewing a complaint against the Saudi crown prince has asked the Argentine Foreign Ministry to seek information from Yemen, Turkey and the International Criminal Court, the judge's office said.
The office of judge Ariel Lijo said it was seeking information on any open cases relating to the murder of Khashoggi or war crimes in Yemen.
The crown prince arrived in Buenos Aires earlier on Wednesday for a summit of G20 nations.