Houthi fighters ride a truck near the presidential palace in Sanaa on Jan. 22. While the Houthis are hostile toward al-Qaeda in the Arabian Peninsula they’re also hostile toward the U.S. (Khaled Abdullah/Reuters)

The White House’s strategy for fighting al-Qaeda in Yemen — repeatedly presented as a model by President Obama — was left in tatters Thursday by the resignation of the manwho personally approved U.S. drone strikes in the country and the collapse of its central government.

U.S. officials struggled to sort out a melange of reports about who, if anyone, is in charge in Yemen. The prospect of continued chaos cast doubt on the viability of the Obama administration’s counterterrorism policy for Yemen and whether it can still count on local help against al-Qaeda.

“A dangerous situation just went from bad to worse with grave implications for our counterterrorism efforts,” said Rep. Adam B. Schiff (D-Calif.), a member of the House Intelligence Committee. “Our relationship with the Yemen government has been vital in confronting [al-Qaeda] and keeping the pressure on its leadership, and every effort must be made to continue that partnership.”

As recently as September, Obama had cited his Yemen strategy as a template for confronting jihadist threats in other places, including Iraq and Syria. Instead of sending large numbers of troops to fight al-Qaeda’s affiliate in the country directly, the Pentagon has limited its presence to a small number of trainers to teach and equip Yemen’s security forces.

The other foundation of the U.S. strategy has been to rely on drones to provide surveillance over Yemen and launch scores of airstrikes against suspected al-Qaeda in the Arabian Peninsula (AQAP) targets. Flown by the CIA and the military’s Joint Special Operations Command, the drones are based outside Yemen, but U.S. officials have relied until now on the Yemeni government’s authorization to conduct the airstrikes.

If order and a friendly regime are not restored soon in Yemen, the White House may be confronted with a difficult choice: keep flying the drones even if they violate Yemeni sovereignty, or halt the operations and ease up on al-Qaeda. The dilemma is exacerbated by the fact that the CIA and U.S. military’s targeting decisions are largely dependent on Yemeni government intelligence collected from sources on the ground.

“I have a lot of sympathy for anybody trying to make a policy on Yemen at the moment,” said Stephen A. Seche, who served as U.S. ambassador there from 2007 until 2010. If a power vacuum persists or no reliable partner emerges to take charge of the government, he added, “I don’t think we’ll just want to continue running operations like we have done the last several years.”

Despite widespread anger among Yemenis about the drones, the Obama administration had received a green light for the airstrikes from Yemeni President Abed Rabbo Mansour Hadi, who took power in 2012 with Washington’s backing and quickly became a firm ally against AQAP.

In an interview with The Washington Post several months after taking office, Hadi said he personally approved every drone strike and praised their effectiveness. “Every operation, before taking place, they take permission from the president,” he said at the time.

On Thursday, Hadi submitted his resignation, along with the rest of his cabinet, under pressure from Houthi rebel forces who have taken increasing control of the capital, Sanaa.

One of Hadi’s advisers, Sultan al-Atwani, said the president quit after the Houthis tried to strip him of virtually all of his powers, including his authority to coordinate drone strikes with U.S. officials.

Although the Houthis are hostile toward AQAP, they have been just as hostile toward the United States.

“The Houthis will refuse to cooperate with the United States in carrying out drone attacks,” said Ali Shantoor, a retired Yemeni brigadier general. “They’ve always said that they reject the United States’ control and its violation of the sovereignty of the country.”

In Washington, U.S. officials dodged questions about whether they had been in contact with Hadi or how his departure will affect counterterrorism operations.

“Obviously, we’re not in a position — and I don’t think any of you are, either — to assess what it means at this point in time,” State Department spokeswoman Jen Psaki told reporters.

The Pentagon has never fully disclosed how many military personnel have been deployed to Yemen as trainers or liaison officers. On Thursday, Maj. Curt Kellogg, a military spokesman, declined to say how many U.S. personnel remained in Yemen or if their numbers had decreased recently because of the upheaval there.

Rep. Mac Thornberry (R-Tex.), the chairman of the House Armed Services Committee, said Thursday that U.S. surveillance over Yemen has decreased in recent months because of increased demand for drones and other aircraft to fight another jihadist group, the Islamic State, in Iraq and Syria.

“Yemen’s a pretty big mess,” Thornberry said. “You have this big, very difficult crisis with [the Islamic State], so that necessarily means there is less attention that can be paid to Yemen and other places. And yet Yemen is the place from which the most serious threats against our homeland have emanated.”

On Thursday, a senior State Department official said the U.S. Embassy in Sanaa would further reduce its American staffing “in response to the changing security situation in Yemen.” The official said the embassy would remain open.

Hugh Naylor in Beirut and Ali al-Mujahed in Sanaa contributed to this report.