Saudi Arabia launched a new round of airstrikes in Yemen on Wednesday, amid U.S. concerns that the nearly four-week operation has outlived its military usefulness and become counterproductive to a political settlement.

As heavy bombing of Houthi rebel positions was reported in Taiz, in southwest Yemen, Saudi Arabia’s ambassador to the United States said his government would also take action to stop rebel forces­ who were moving into the port city of Aden from three directions.

The strikes came just a day after the Saudi government announced that its air campaign had achieved its goals of eliminating threats from across its southern border by destroying aircraft, missiles and heavy weapons seized from the Yemeni government by rebel fighters who forced President Abed Rabbo Mansour Hadi to flee last month. The Saudis said that military operations would shift to humanitarian assistance and forging a political solution to the conflict.

But Saudi Ambassador Adel al-Jubeir, speaking Wednesday in Washington, said that his government would continue to act to “protect [Yemeni] civilians and counter aggressive moves” by the Houthis and breakaway Yemeni military forces­ allied with them.

“The decision to calm matters now rests entirely with the Houthis,” Jubeir said at a news conference. He also called on Iran, which is widely believed to support the Houthis, to “be wise and not add to the problems.”

The Houthis said in a statement that they might be interested in resuming a political dialogue, but not until there is “a complete end to the aggression against Yemen.”

The United States is continuing to provide intelligence and logistics support to the Saudi air campaign, a senior Obama administration official said. But the operation is “reaching the point where there are diminishing returns and, in some cases, negative returns in terms of the humanitarian impact,” said the official, one of several who discussed U.S. concerns on the condition of anonymity because of diplomatic sensitivities.

That message has been repeatedly conveyed to Riyadh in conversations between high-level U.S. and Saudi diplomatic and military officials over the past week, and the Obama administration was assured by Monday that the air campaign would end within 24 to 48 hours. Without a ground force to seize and hold territory from the Houthis and their allies, the Saudis were running out of stationary targets, U.S. officials said.

While it was initially important that the Saudis “targeted offensive weapons . . . the stuff [the Houthis] could use,” a second administration official said, “we think we’ve reached the end of its effectiveness.”

Humanitarian concerns have grown about civilian casualties, dire shortages of food, water and fuel, and the virtual collapse of Yemen’s transportation and health-care infrastructure. At the same time, U.S. officials have grown increasingly worried that the campaign against the Houthis is hurting the effort against Yemen-based Al-Qaeda in the Arabian Peninsula, or AQAP.

U.S. officials declined to discuss reports from Yemen that an American drone strike on Wednesday had killed seven suspected AQAP fighters in Mukalla, on the south-central coast, where the Associated Press reported that the militants have recently made advances­ and struck deals with local tribesmen.

“I can’t speak to any operation that may have taken place,” an administration official said of the reported strike, but AQAP remains “our number one national security priority in Yemen.” While the United States retains the ability to act against the group despite the withdrawal of U.S. military forces there, “the chaos on the ground has made that more difficult,” the official said.

U.S. support for the Saudi operation has been aimed in large part at reassuring Riyadh that U.S. nuclear negotiations with Iran, its chief regional rival, would not result in a shift of American alliances in the region. At the same time, other regional partners share the U.S. concern that the Yemeni conflict could escalate into a growing sectarian conflict like those in Syria and Iraq.

Both Iran’s population and the Houthis are Shiite; Saudi Arabia and the rest of the Persian Gulf are majority Sunni.

The Saudi military has blocked Yemeni ports and airspace to prevent what it says has been a steady flow of arms and other supplies from reaching the Houthis. Both the United States and Iran, saying they want to protect international sea lanes, have sent naval vessels to the Gulf of Aden.

President Obama, in an MSNBC interview broadcast Tuesday night, said that “if weapons are delivered to factions in Yemen that could threaten navigation, that’s a problem.” He said that “we’re not sending obscure messages” to Iran, “we’re sending very direct messages.” Secretary of State John F. Kerry is expected to meet next week in New York with his Iranian counterpart.

But while the United States has been concerned “since day one . . . about Iranian support to the Houthis,” it does not share Saudi Arabia’s belief that Tehran is controlling rebel movements in Yemen, an administration official said.

“We believe that the Houthis decided to take Sanaa,” the Yemeni capital they conquered in September, “and decided to move south against the advice of the Iranians,” the official said.

The Houthis’ move beyond their traditional tribal region in northern Yemen along the Saudi border has been aided by military forces loyal to former Yemeni president Ali Abdullah Saleh.

Saudi Arabia, the United States, the United Nations and others have called for all parties in Yemen, including the Houthis, to participate in a dialogue to be held in a third country.

Jubeir, the Saudi ambassador, said that any political solution must include restoring Hadi to power. “He is the president of Yemen and will remain president of Yemen until the people of Yemen go through their political process and choose new” leadership, Jubeir said.

But Hadi’s return appears increasingly unlikely as fighting continues to rage.

Wadhah al-Dubaish, 40, an anti-Houthi fighter in Aden, said that clashes­ continued to erupt across the besieged city, where he and other fighters have expressed frustration over the embattled president’s decision to escape to Saudi Arabia.

“Hadi better not dream of coming to Aden,” Dubaish said by telephone, adding: “We will continue to fight until we drive out the Houthis or kill them.”

Mujahed reported from Sanaa, Yemen. Hugh Naylor in Beirut contributed to this report.

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