US President Donald Trump has been asked to ascertain whether Saudi Crown Prince Mohammed bin Salman played a role in the murder of Jamal Khashoggi.
Republican and Democratic leaders of the US Senate Foreign Relations Committee on Tuesday sent a letter demanding a second investigation.
Mr Trump earlier defended US ties with Saudi Arabia despite international condemnation over the incident.
Khashoggi was killed on 2 October inside the Saudi consulate in Istanbul.
In a statement on Tuesday, Mr Trump acknowledged that the crown prince "could very well" have known about Khashoggi's brutal murder, adding: "Maybe he did and maybe he didn't!"
He later stated that the CIA had not made a "100%" determination on the killing.
The journalist who vanished into a consulate
The Jamal Khashoggi story so far
Following the president's comments, Republican Senator Bob Corker and Democrat Bob Menendez issued a statement on behalf of the Senate Foreign Relations Committee.
In it they called on Mr Trump to focus a second investigation specifically on the crown prince so as to "determine whether a foreign person is responsible for an extrajudicial killing, torture or other gross violation" of human rights.
The request, issued under the Global Magnitsky Human Rights Accountability Act, requires a response within 120 days.
Saudi Arabia has blamed Khashoggi's death on rogue agents but denied claims that the crown prince had knowledge of the operation.
US media have reported that the CIA believes Mohammed bin Salman ordered the murder.
In an interview on Sunday, Mr Trump told Fox News that he had refused to listen to a recording of Khashoggi's murder provided by Turkey, calling it "a suffering tape".
A dark shadow for years to come
By the BBC's chief international correspondent, Lyse Doucet, in Riyadh
For Saudis, and especially Saudi leaders, there will be a sigh of relief. But, it's also what they expected, and what they've always said about President Trump - he will be a true friend of the Kingdom.
Both sides want to draw a line under this major crisis - and global outcry. But as Mr Trump acknowledged, and Saudis know, it won't go away. Not for many in the US Congress, as well as for many others, including countries who will continue to call for greater clarity.
Many Saudis say they don't believe their country's de facto ruler, Crown Prince Mohammad Bin Salman, would have ordered such a despicable act. Many, who'd long been hoping to see their country move forward, have been shaken by this shocking murder, and regret it will cast a dark shadow for many years to come.
In the words of one prominent Saudi: "It has brought Saudi Arabia ten steps back."
Meanwhile, Lindsey Graham, a senator from Mr Trump's Republican Party, has predicted strong bipartisan support in Congress for sanctions against Saudi Arabia "including appropriate members of the royal family".
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