(CNN) Bipartisan frustration mounted on Capitol Hill Tuesday over the Trump administration's handling of an overdue investigation into who killed Jamal Khashoggi and whether Saudi Crown Prince Mohammed bin Salman should be held responsible and sanctioned under the Magnitsky Act.

"Worthless," is how Sen. Lindsey Graham, a Republican from South Carolina, described a classified update on the administration's probe, which took place Monday.

"Miserable," is what Sen. Chris Murphy, a Democrat from Connecticut, called it.

Sen. Bob Menendez, the top Democrat on the Senate Foreign Relations Committee, called Monday's briefing "a waste of time" and "a sham."

Democratic Sen. Tim Kaine of Virginia charged the administration is not taking the Khashoggi murder seriously and is not complying with demands of the law.

"I think the administration, specifically the President, is in violation of the Magnitsky Act," he said.

The criticism comes ahead of a key confirmation hearing this week for President Donald Trump's nominee to be US ambassador to the kingdom.

Senate Foreign Relations Chairman Jim Risch, a Trump ally who is working with administration to get answers, acknowledged there are concerns on both sides of the aisle.

"I've never been in a briefing yet where people were completely satisfied. Having said that, there is certainly a lot more work to be done. It's a work in progress," the Idaho Republican said. "There isn't anybody happy really with the situation the way it is."

The administration skipped a deadline last month when it was supposed to send a report to Congress, as called for by the Global Magnitsky Human Rights Accountability Act, detailing who is responsible for the murder.

US sanctions have been imposed on 17 Saudi individuals but not bin Salman.

A Senate Democratic source told CNN that lawmakers were briefed again on the 17 Saudi individuals impacted by those measures but that the individual sent by the administration had no answer to questions about the Magnitsky invocation.

"It was a total joke and it backfired," the source said, adding that the briefing only served as more bipartisan fuel to pursue legislative measures aimed at holding the Saudi regime and Crown Prince responsible.

Risch said he spoke to Secretary of State Mike Pompeo for about 30 minutes Tuesday to discuss the administration's ongoing efforts to respond to Congress.

He also met with retired Gen. John Abizaid, Trump's choice to be his ambassador to Saudi Arabia who will testify before Risch's committee Wednesday, a forum senators likely will use as to voice their dissatisfaction.

Risch wouldn't say if the administration is still maintaining that bin Salman is not responsible for Khashoggi's death.

"The real issue is what do we do about Saudi Arabia. Because this was state action. It was not individual's actions," Risch said. "All the 17 people who were sanctioned have been identified as people who were working for the Saudi government."

Risch, who became chairman of the committee just three months ago, is trying to delicately balance the demands his Senate colleagues have for answers with the needs of the administration to finish its probe into alleged criminal acts by an important ally in a strategic part of the world.

Asked if he believes bin Salman is responsible, Risch said, "I'm just not going to go there. What I will tell you is: Certainly, he is the head of the country and the country did this, so the head of the country always has to speak for it."

Leaving the briefing Monday, Sen. Marco Rubio, a Florida Republican, told CNN he was not pleased.

"It's not the right approach to it -- I've said that from the beginning," he said, while adding that Trump officials are saying privately what they are saying publicly about bin Salman's role in the murder: "They have no direct evidence."

Sen. John Barrasso of Wyoming, a member of GOP leadership who rarely criticizes Trump, said as he was departing the briefing, "I'm not happy with the results."

Kaine, who sits on the Foreign Relations Committee, said senators in both parties are not confident Trump will ever meet his requirements under the Magnitsky Act.

"He was required to certify to Congress whether or not MBS was culpable, in the context of the statute, for the death of Jamal Khashoggi," he said. "He has chosen not to do that."

Kaine added, "There's an awareness by everybody on the committee that the President is thus far not complying with the law. And we have no idea about whether he ever will."

But Risch disagreed, saying he did not think the administration was in violation.

"No, I really don't," he said. "There was a request made for them to do things and they did some things. There are others they are still working on. So, I don't think anyone could say they are definitively in violation of the Magnitsky Act."

Senators said it wasn't clear what steps they could take to compel Trump to comply.