But the proposals put forth by Pompeo and Mattis are burdened by strategic limitations.

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Mattis called for a cease-fire in which the rebels would pull back from Yemen’s border with Saudi Arabia and start negotiations within 30 days. But he also said Saudi Arabia had a right to defend itself against Houthi missiles, which U.S. officials say have been supplied by Iran.

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Pompeo proposed that the rebels first stop firing missiles at Saudi Arabia and the UAE and that Saudi Arabia then stop airstrikes that have killed thousands of civilians.

“It is time to end this conflict, replace conflict with compromise, and allow the Yemeni people to heal through peace and reconstruction,” Pompeo said.

The urgency of that appeal reflects the complexity of U.S. interests on the Arabian Peninsula, weeks after Pompeo certified to Congress that Saudi Arabia and the UAE were making progress on reducing civilian casualties in Yemen. The report was required because the United States helps the Saudi-led coalition refuel its jets and shares intelligence with its military officials.

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But neither U.S. official’s statements had an “or else” attached to it, former officials said.

“If you give your closest ally a pass and say, ‘You don’t need to do anything until the enemy takes the first step,’ that is not a serious proposal,” said Stephen Seche, a former U.S. ambassador to Yemen who now is executive vice president of the Arab Gulf States Institute in Washington. “You’ve got to propose both parties need to move simultaneously to implement a cease-fire.”

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It also was unclear who might lean on the Houthis and Iran, especially as Tehran faces the reimposition of U.S. sanctions next week after President Trump’s withdrawal from the 2015 nuclear deal.

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“This won’t happen by spontaneous combustion,” said Aaron David Miller, a Middle East scholar at the Wilson Center, calling the administration’s initiative intriguing but “half-baked.”

“Remember, next week, oil sanctions kick in,” Miller said. “And Tehran will want something in return for leveraging their Houthi ally.”

But humanitarian organizations expressed relief, sensing a glimmer of hope that the fighting that has killed more than 10,000 civilians may have a potential end in sight.

Even as the Trump administration intensifies pressure to end the war, the Saudi-led coalition has sent thousands of additional troops to the front lines near the strategic port city of Hodeida. That raises the possibility of a punishing urban battle that could add to civilian suffering.

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The coalition has made capturing the city from the Houthis a priority, in part because it says the rebels have used the port to smuggle in Iranian-supplied weaponry.

Mattis has mentioned the war several times in recent days and highlighted the human suffering in a weekend speech in Bahrain.

“Now is the time to move forward on stopping this war,” he said last weekend, while also lauding Saudi efforts to ensure an accurate air operation and citing the difficulty of avoiding unintended deaths when targeting militants from afar.

On Tuesday, speaking at the U.S. Institute of Peace, Mattis said with a note of urgency: “We’ve got to move towards a peace effort here, and we can’t say we’re going to do it sometime in the future. We’ve admired this problem for long enough down there.”

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Pompeo weighed in Tuesday night, expressing support for U.N. special envoy Martin Griffiths, who has called for negotiations to convene in November.

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“The time is now for the cessation of hostilities, including missile and [drone] strikes from Houthi-controlled areas into the Kingdom of Saudi Arabia and the United Arab Emirates,” he said in a statement. “Subsequently, Coalition airstrikes must cease in all populated areas in Yemen.”

The officials’ remarks were stronger than anything the administration has said about Yemen in the past 17 months.

Pompeo came under criticism last month when he backed continuing arms sales to the Saudis, reportedly after concerns were raised that a cutoff could affect billions of dollars in such sales to the kingdom.

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Since then, events have converged to push the Trump administration to alter its public stance on Saudi Arabia and Yemen.

The administration appears to be trying to get in front of proposals in Congress to curtail U.S. support, with critics emboldened by the international outrage over the killing of Washington Post contributing columnist Jamal Khashoggi by a team of Saudi agents.

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“It’s hard not to think there is some kind of association here,” said Seche, the former U.S. ambassador. “Something other than just a sudden desire to see war end. A wave of indignation that has swept over Saudi Arabia because of the killing of Jamal Khashoggi has got to have some impact on our thinking, given our close association with the Saudis in Yemen as the preferred supplier of weapons and logistical support. It implicates the United States in this humanitarian crisis. It’s time to get ahead of the wave.”

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The administration statements come as both parties in Congress press for an end to U.S. involvement in the conflict.

Among those from the president’s party who have questioned the current policy are Sens. Todd C. Young (Ind.) and Rand Paul (Ky.), and more recently Sens. Ben Sasse (Neb.), Lindsey O. Graham (S.C.) and Marco Rubio (Fla.).

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In the House, Rep. Ro Khanna (D-Calif.) has introduced a measure, now supported by senior Democrats, that would halt U.S. involvement in the conflict under the War Powers Act.

Gerald Feierstein, another former ambassador to Yemen, said the changing analysis in Congress could transform U.S.-Saudi ties, particularly when it comes to arms sales.

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“People are really questioning the whole nature of the relationship,” he said.

Saudi Arabia is one of the world’s largest purchasers of advanced weaponry and an important customer for U.S. defense firms.

Feierstein said the administration may have another motive to want a swift end to the hostilities: It would alleviate pressure on the administration to take broader punitive action against Saudi Arabia in the wake of Khashoggi’s death. If American-made Saudi weapons are not being used in Yemen, it will be easier for U.S. arms sales to the kingdom to continue.

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Robert Malley, who was a senior White House official under President Barack Obama and now serves as president of the International Crisis Group, said the Trump administration had closely embraced the Persian Gulf kingdom, smoothing over differences from the previous administration and elevating its position as a central Middle Eastern ally.

“What’s been missing is getting something out of that hug,” he said. “This could reestablish some balance.”

Michael Knights, a senior fellow at the Washington Institute for Near East Policy, said he worries that a push for a cease-fire to alleviate political pressure could paper over the fissures driving the war. But he said a cease-fire and negotiations now have a decent chance to succeed.

“Because international support for this war is about as low as you can get,” he said, “the United States is under severe pressure from its own congressional branch, and military progress in the war is limited. The U.N. envoy is very active and quite effective.”

“And exhaustion may be a factor,” he added. “That improves the chances of a settlement.”