(CNN) President Donald Trump said Friday that he believes Saudi Arabia's explanation for the death of journalist Jamal Khashoggi and called the arrest of 18 Saudis "a good first step."

The Saudi Arabian government announced Friday that Khashoggi died after a fistfight at the Saudi consulate in Istanbul, and that 18 Saudis had been arrested for further investigation while Deputy Director of Saudi Intelligence Ahmed al-Assiri had been dismissed.

"I do. I do," Trump said when asked about his confidence in the explanation. "Again, it's early. We haven't finished our review, our investigation. But I think it's a very important first step."

Trump said talks with Saudi officials would continue, including raising some questions about their account of events that led to the death of Khashoggi, and that he would work with Congress to develop a response.

However, lawmakers from both sides of the aisle on Capitol Hill expressed skepticism over Saudi Arabia's professed explanation for Khashoggi's disappearance.

Sen. Richard Blumenthal accused the Saudis of "buying time and buying cover," calling for an investigation that included US involvement and Turkish audio and visual records of the event.

"The Saudis very clearly seem to be buying time and buying cover, but this action raises more questions than it answers," the Connecticut Democrat told CNN's Wolf Blitzer on "The Situation Room" Friday night.

"There has to be an international investigation," he continued. "It has to be done with legitimate and credible means involving the United States, and it has to use those tapes, the surveillance that evidently the Turks have."

Blumenthal also accused the Saudi government of trying to "insulate and shield" Saudi Arabian Crown Prince Mohammed Bin Salman, known as MBS, and protect the 18 arrested Saudis from further investigation.

"The world deserves an explanation, not from the Saudis, who evidently are making every effort to insulate and shield the crown prince, but from an international inquiry," Blumenthal said, adding that the group arrest "raises the possibility that they may put them in a kind of protective custody and insulate them from an international investigation, shield them from fact-finding that the world needs to do."

New Jersey Sen. Robert Menendez, the top Democrat on the Senate Foreign Relations Committee, said in a statement that the Saudi statement is "far from the end."

"This is far from the end and we need to keep up the international pressure. Congress did its part when we invoked Global Magnitsky Act for a presidential determination. Now President Trump must follow the law," Menendez said.

Senate Foreign Relations Committee chairman Sen. Bob Corker warned against assuming that the Saudis' "latest story holds water" and stressed that the U.S. must assess Khashoggi's death under the Global Magnitsky Act, which sanctions human rights offenders.

"The story the Saudis have told about Jamal Khashoggi's disappearance continues to change with each passing day, so we should not assume their latest story holds water," Corker tweeted Friday . "They can undergo their own investigation, but the U.S. administration must make its own independent, credible determination of responsibility for Khashoggi's murder under the Global Magnitsky investigation as required by law."

Republican South Carolina Sen. Lindsey Graham also questioned the credibility of the Saudis' changing explanation.

"To say that I am skeptical of the new Saudi narrative about Mr. Khashoggi is an understatement," Graham tweeted Friday . "First we were told Mr. Khashoggi supposedly left the consulate and there was blanket denial of any Saudi involvement. Now, a fight breaks out and he's killed in the consulate, all without knowledge of Crown Prince."

"It's hard to find this latest 'explanation' as credible," he added

Republican Kentucky Sen. Rand Paul called for Saudi Arabia to pay "a severe price" for Khashoggi's death.

"We should ... halt all military sales, aid and cooperation immediately," Paul tweeted . "There must be a severe price for these actions by Saudi Arabia."

On the House side, both Republican and Democratic lawmakers called on Trump to act.

Colorado Republican Rep. Mike Coffman called on the administration to take a stronger stance in responding to Khashoggi's death.

"Our country must stand up for our values and demand our 'allies' respect human rights," the House Armed Services committee member wrote in a statement on Twitter

"The United States and the rest of the international community must condemn the murder of Mr. Khashoggi and the use of diplomatic posts as torture chambers for rogue nations," Coffman added. "I am calling on President Trump to immediately recall the (Acting) U.S. Ambassador to the Kingdom pending further consultation with Congress."

Rep. Gerry Connolly said that the Saudi statement sounded "almost like a classic mafia operation."

"Now they're engaged in a cover up to protect the Crown Prince, and we'll see how that works for them," the Virginia Democrat told CNN's Kate Bolduan on "Erin Burnett OutFront". "There is no way this kind of premeditated murder operation conceivably have happened in the Saudi consulate without the knowledge of and approval of the Crown Prince."

When asked if Congress would take action, Connolly said there was sufficient bipartisan "outrage," but still criticized Trump's handling of the incident from the beginning.

"Wouldn't it be nice if we had a president who actually held murderers to account?" he added.

Democratic Rep. Eliot L. Engel, ranking member of the House Committee on Foreign Affairs, called for Trump to more actively pursue "a thorough and transparent investigation."

"Tonight's explanation from Saudi authorities just isn't credible, particularly since the story has shifted so much over the past days," Engel wrote in a statement. "The Administration needs to push for a thorough and transparent investigation into Mr. Khashoggi's death without delay."