"The relationship between the USA and Saudi Arabia can not move forward until Crown Prince Mohammed bin Salman is dealt with", Graham said.
On Friday, Graham had met with Turkish President Tayyip Erdogan, who has reacted angrily to Khashoggi's killing in Istanbul.
Riyadh, which initially denied knowledge of Khashoggi's disappearance, then offered contradictory explanations, has described the assassination as a "rogue operation", though the Central Intelligence Agency has concluded that bin Salman (MBS) nearly certainly signed off on the mission.
The Republican lawmaker said that ties between the two sides can not move forward unless action was taken against Bin Salman, who faced worldwide rebuke over his role in the murder of his supporter-turned-critic and Washington Post contributor Jamal Khashoggi at the kingdom consulate in Turkey in October.
Graham also said Congress will reintroduce sanctions against those involved in the killing of Khashoggi.
Saudi officials have said the crown prince knew nothing of the killing.
As per house "Crown Prince Mohammed loves risk and is eager to turn page from the Jamal Khashoggi murder".
Cancela Trump viaje a Pelosi 'de último minuto'
Asimismo, el presidente apuntó en sus declaraciones que el Partido Demócrata ha sido "secuestrado" por la "izquierda radical" liderada por Pelosi .
Earlier this month the trial of 11 accused opened in Saudi Arabia with the attorney general seeking the death penalty for five defendants.
The United States imposed economic sanctions on 17 Saudi officials in November for their role in the Khashoggi killing. Ties have also been strained by the Senate's vote to push for ending military support for the Saudi-led coalition in the war in Yemen.
"You make people we're trying to help wonder about us". Graham's latest comments come as tensions in the region run high amid US plans to withdraw troops from Syria.
"I would hope that President Trump would slow the withdrawal until we truly destroy ISIS", said Graham, using an alternative acronym for IS.
The president's decision unleashed a war of words between Ankara and Washington, amid U.S. fears of a Turkish offensive against the Kurdish People's Protection Units (YPG), a US-backed force that has been fighting IS.
Graham also said in Ankara that by arming the YPG group in Syria, Washington had "created a nightmare for Turkey".
ISIS killed two USA service members and two American civilians in the northeastern town of Manbij in a suicide bombing just days before the visit.