Along with Republican colleagues, lawmakers have denounced Prince Mohammed for the murder of Mr. Khashoggi — in which he has vehemently denied playing any role — and the mass killing of civilians in the war in Yemen. A top Democrat in the Senate, Robert Menendez of New Jersey, has placed a hold on the sale of certain weapons to Saudi Arabia.
Lawmakers have also expressed apprehension over any move by Saudi Arabia to enrich uranium in its territory, citing proliferation concerns. For years, the State Department has been trying to negotiate what it calls a 123 agreement with the Saudis, which would lay out tough nonproliferation criteria to allow for American cooperation on civilian nuclear energy, though Saudi officials have balked at the restrictions in part because of Iran’s program. The United States has such an agreement with the United Arab Emirates, Saudi Arabia’s neighbor, that bans in-country uranium enrichment.
But Democratic and Republican lawmakers are generally supportive of promoting normalization between Israel and Arab nations, and they know that such accords can be a political gain to win over pro-Israel voters during election seasons.
Aides working for the two top senators on the Senate Foreign Relations Committee, Mr. Menendez and Jim Risch, Republican of Idaho, are drafting a bill that calls for the U.S. government to try to deepen the Abraham Accords and expand what they call “regional integration.”
Among the Republicans, an unlikely figure has stepped forward offering to help: Mr. Graham. In an interview, he said he has been working with top Biden administration officials to help to broker Saudi-Israeli peace.
“Ending the Arab-Israeli conflict would be a game changer for the world and further isolate Iran,” he said.
Mr. Graham says he has spoken to Senator Mitch McConnell, the Kentucky Republican and minority leader, and other top G.OP. lawmakers, and said there would potentially be “a lot of support on the Republican side.” He met with Prince Mohammed in Riyadh earlier this year, and has frequent discussions with senior Israeli officials.