Washington (CNN) The United States is working to capitalize on what it regards as new leverage with Saudi Arabia to end the brutal civil war in Yemen and ease a regional standoff with Qatar, according to multiple US and diplomatic officials.

Seeing an opening created by the kingdom's new pariah status after the killing of a dissident journalist , US officials say the time is ripe to move on longstanding goals, including forcing an end to the Saudi-led bombing campaign that has prompted a humanitarian crisis in neighboring Yemen.

The officials acknowledged that neither the Yemen war nor the dispute with Qatar can be solved quickly. But the administration hopes to make progress on both fronts by the end of the year, they said, and have recently stepped up public calls on Saudi Arabia to alleviate the disputes.

Calls for Yemen ceasefire

Secretary of Defense Jim Mattis and Secretary of State Mike Pompeo both this week called on participants in the Yemen civil war to agree to a ceasefire "in the next 30 days," a demand that comes amid fresh criticism of US support for the Saudi-led coalition in the conflict.

"Thirty days from now we want to see everybody around a peace table based on a ceasefire, based on a pullback from the border and then based on ceasing dropping of bombs," Mattis said at an event at the US Institute of Peace in Washington on Tuesday.

His call was later echoed by Pompeo, who issued a statement saying, "the United States calls on all parties to support UN Special Envoy Martin Griffiths in finding a peaceful solution to the conflict in Yemen."

Mattis and Pompeo both insisted that the US-backed Saudi-led coalition and the Iranian-aligned Houthis stop their respective aerial and missile bombardments.

The three-year conflict between Saudi-led coalition and their Iranian-backed enemies has devastated Yemen and killed at least 10,000 people. United Nations experts say that the coalition's bombing of civilians are potential war crimes and that its partial blockade of the country has put 13 million men, women and children in danger of starvation, in what could become the worst famine in 100 years.

Griffiths said the most pressing factor justifying the US call for a cease-fire was the threat of starvation: "The threat of famine is a very real threat and risks doubling the numbers of people in Yemen who are at risk of dying of hunger or famine. That's the urgent factor here."

Griffiths said he believed the US administration is taking this issue seriously, adding: "Secretary Mattis and Secretary Pompeo are on this day and night" but acknowledged "the challenge now is to turn this call into action."

Outrage over the situation has created increasing pressure on the US to pull its support for the coalition, which it provides in the form of military sales, training and refueling of coalition jets.

Saudi Arabia's belated admission that Jamal Khashoggi, a Washington Post journalist and US resident, was murdered by a team with close ties to Crown Prince Mohammed bin Salman has left the Trump administration -- including the President himself -- feeling stung by Saudi Arabia.

After initial strong denials, the kingdom has produced multiple explanations. Even after admitting that Khashoggi was murdered by men close to bin Salamn, the Saudi Foreign Minister Adel al-Jubeir said blaming Saudis for the US resident's death is "hysterical."

Speaking at the International Institute for Strategic Studies Manama Dialogue in Bahrain Saturday, al-Jubeir said, "This issue has become fairly hysterical. People have assigned blame on Saudi Arabia with such certainty before the investigation is complete. We have made it very clear that we are going to have a full and very transparent investigation, the results of which will be released."

Al-Jubeir met with Mattis on Sunday in Bahrain. The defense secretary told reporters traveling with him on his plane to Prague that he had discussed Khashoggi's death with the Saudi official. "We discussed it," Mattis said, "you know the same thing we talked about, the need for transparency, full and complete investigation, um, full, full agreement from FM Jubeir, no reservations at all, I said we need to know what happened."

Trump and senior adviser Jared Kushner, who is the President's son-in-law, placed a heavy reliance on the powerful crown prince for an overall strategy in the region, despite warnings that the young royal was untested and volatile.

While American officials previously expressed private displeasure at Mohammed's intervention in the Yemen war and the Saudi-ordered kidnapping of Lebanese Prime Minister Saad Hariri, they mostly aired their grievances in private while maintaining in public that the alliance with Saudi Arabia was necessary to counter Iran's influence.

Trump is privately fuming

But Khashoggi's murder, and the ensuing coverup, have made it more difficult to keep those grievances private.

Trump has privately fumed at the Saudis for putting him in the situation of having to defend his decision to fastidiously cultivate a close relationship with Mohammed and his father, King Salman. He and his advisers are in agreement that forcing some kind of resolution on Yemen is a good way to make the best of a bad situation.

The Saudi stand-off with Qatar, which has fractured a security alliance importance to the US, has been another thorn in the Trump administration's side.

Asked Wednesday whether he felt betrayed by the Saudis, Trump suggested it was the kingdom's leaders that betrayed themselves.

"I just hope that it all works out. We have a lot of facts, we have a lot of things that we've been looking at," he said. "They haven't betrayed me. I mean, maybe they betrayed themselves. We'll have to see how it all turns out."

Trump has come to the belief in recent days that the American public is starting to catch on to the Yemen catastrophe, including through powerful images of starving children in the New York Times.

The Trump administration has been criticized by activists and some members of Congress for its support for the Saudi-led coalition fighting the Houthis in Yemen and for the administration's recent finding that the coalition was doing enough to avoid civilian casualties.

The US military provides the Saudi collation with training meant to help minimize civilian casualties, as well as aerial refueling of coalition warplanes.

Mattis said the "goal right now is to achieve a level of capability by those forces fighting against the Houthis, that they are not killing innocent people."

"We refuel probably less than ... I think 20% of their aircraft. They have their own refuelers, by the way," Mattis said.

Congressional pressure

A congressional source told CNN the Khashoggi murder has "put a face" on the broader problem related to the US-Saudi relationship and renewed momentum on Capitol Hill to push for legislation that would end US involvement in the war in Yemen.

Previous resolutions aimed at ending US involvement in the war in Yemen have failed to gain approval but various pieces of legislation proposed in recent months have received increasing support from lawmakers on both sides of the aisle. Sen. Bernie Sanders, a Vermont independent, wrote in a recent op-ed that he plans to bring his resolution to end US involvement in the "unauthorized war" in Yemen back to the floor next month.

"Because of the privileged resolution that will come to a vote sooner or later and that is certainly something that's weighed on the administration," a senior congressional aide told CNN. "I am sure Mattis and Pompeo are well aware of that."

Democratic Rep. Ro Khanna also cited Pompeo's statement in a press release touting his own bipartisan proposal in the House intended to align with the resolution Sanders is pushing in the Senate.

"It's about time. After more than three years of war, thousands dead, millions on the brink of starvation, and growing pressure from Congress, the Trump Administration is finally calling for an end to the Saudi-led war in Yemen," Khanna said in a statement. "We have tremendous leverage over the Saudi-led coalition and should demand this Administration do all in their power to bring both sides to the peace table and end the war."

The congressional source also told CNN that efforts to curtail US involvement in Yemen and pressure to respond to Khashoggi's murder are related in that they both provide evidence of the Saudi government's and in particular the crown prince's "recklessness."