Senator Bob Corker, the Tennessee Republican who heads the Foreign Relations Committee and sponsored the measure condemning the crown prince, said on Thursday that it was vital that the Senate “is speaking with one voice” to hold him accountable.

“Unanimously, the United States Senate has said that Crown Prince Mohammed bin Salman is responsible for the murder of Jamal Khashoggi,” Mr. Corker said. “That is a strong statement. I think it speaks to the values that we hold dear.”

Senators in both parties described the twin measures as a direct response to the refusal by Mr. Trump and his administration to hold Saudi Arabia to account for Mr. Khashoggi’s death — and a way to counter the president’s assertion that the money to be made from arms sales to the kingdom was enough to justify turning a blind eye to such a deed.

“We cannot sweep under the rug the callous disregard for human life and flagrant violations of international norms the Saudis are showing,” said Senator Robert Menendez of New Jersey, the senior Democrat on the Foreign Relations Committee.

“A few more weapons purchases cannot buy our silence — it should not buy our silence,” Mr. Menendez said. “And if the president will not, Congress must act.”

The votes came only hours after Defense Secretary Jim Mattis and Secretary of State Mike Pompeo implored members of the House of Representatives during a closed-door briefing to continue the military advising, logistics support and intelligence that have for years been shared with Saudi Arabia.

Some lawmakers emerged from the House meeting frustrated that Mr. Pompeo and Mr. Mattis had defended the United States’ relationship with the kingdom, which the White House needs to counter growing Iranian influence in the Middle East.

Representative David Cicilline, Democrat of Rhode Island, said the two top administration officials had warned against jeopardizing the Saudi partnership — given what they described as a continuing, open investigation into whether Prince Mohammed had, in fact, ordered the killing of Mr. Khashoggi, a Washington Post columnist who had lived in the United States.

“The briefing was a colossal waste of time,” Mr. Cicilline told reporters afterward.

Some senior Republicans offered the administration officials more support.

Representative Steve Scalise of Louisiana, the No. 3 Republican in the House, said Mr. Pompeo and Mr. Mattis had explained details of the investigation into Mr. Khashoggi’s death, as well as complexities of the relationship with Saudi Arabia.

“There needs to be action,” Mr. Scalise said, without elaborating. “We need to hold everyone accountable.”

Mr. Mattis and Mr. Pompeo gave a similar briefing to the Senate late last month. But it broke down as Republican and Democratic senators grew irritated with the administration’s defense of Prince Mohammed. By contrast, after Gina Haspel, the C.I.A. director, briefed senators last week on the case, they emerged saying they were even more convinced of Prince Mohammed’s role.

The measure limiting war powers in Yemen has been under consideration for months, but senators sharpened its language two weeks ago with a procedural vote that signaled their deep frustration over the Trump administration’s refusal to blame Prince Mohammed for Mr. Khashoggi’s killing.

“The relationship with the crown prince is so toxic, so tainted, so flawed that I can’t ever see myself doing business with Saudi Arabia in the future unless there is change there,” Senator Lindsey Graham, Republican of South Carolina, told reporters on Wednesday as debate on the measure began.

But Mr. Graham and other senators sought to separate the importance of maintaining a close alliance and partnership with Saudi Arabia from punishing Prince Mohammed.

Before the killing and dismemberment of Mr. Khashoggi, most Republicans had supported the military alliance between the United States and Saudi Arabia.

But in the Saudi-led campaign in Yemen, to which the Pentagon has supplied bombs and intelligence, Saudi airstrikes targeting Houthi rebels have also killed thousands of people at weddings, at funeralsand on school buses.

In late October, Mr. Mattis and Mr. Pompeo had called for a cease-fire in Yemen, and on Thursday, talks that were brokered by the United Nations in Sweden appeared to reach an agreement to ease the hostilities.

The agreement calls for an exchange of up to 15,000 prisoners, the creation of a humanitarian corridor into the city of Taiz and, importantly, the withdrawal of troops from Hudaydah. That city, on the Red Sea, is a key entry point to Yemen for essential products like food and medicine.

Peace talks are expected to continue in January in an effort to resolve what has become a humanitarian crisis in one of the poorest nations on Earth.

“The agreements today mean a lot, not only for the Yemeni people but for humanity if this can be a starting point for peace and for ending the humanitarian crisis in Yemen,” António Guterres, the United Nations secretary general, said at the close of the talks on Thursday.

Mr. Menendez and Mr. Graham said on Wednesday that they and other senators would introduce legislation early next year to impose even broader penalties against Saudi Arabia, including suspending weapons sales and cementing a ban on American refueling of Saudi coalition aircraft in Yemen.

While Thursday’s moves were largely a symbolic, if stinging, slap at the Trump administration, they previewed what could be a far more consequential debate after Democrats take over the House in 2019.

“If Paul Ryan thinks on his way out the door his last public service gift to humanity is covering up for Saudi Arabia, great, he can make that his legacy,” said Senator Tim Kaine, Democrat of Virginia, referring to the procedural gambit by Mr. Ryan, the House speaker, this week to prevent the war powers measure from coming up for a swift a vote.

“But we’re going to be around next year,” Mr. Kaine said, “and we’ll figure out ways that there can be consequences for this.”