Sanaa, Yemen ? Al-Qaida’s branch remains a powerful threat in this deeply unstable nation, even after a U.S. drone strike that eliminated three of its key figures. Its military leadership remains intact and is only growing stronger amid months of political turmoil tearing Yemen apart.

As the president struggles to keep power, Islamic militants have taken advantage of the government’s crumbling control to take over several cities in the south, raising the danger they can establish a permanent stronghold. On Saturday, militants holding Zinjibar, a southern provincial capital, battled government forces in fighting that killed at least 28 soldiers and militants.

Yemen is considered a crucial battleground with the terror network. The impoverished nation on the southern tip of the Arabian Peninsula is on the doorstep of Saudi Arabia and the oil-producing nations of the Gulf and lies on strategic sea routes leading to the Suez Canal. But order has crumbled as President Ali Abdullah Saleh faces more than seven months of protests demanding an end to his 33-year authoritarian rule, and his loyalists have battled with military units and tribal fighters who sided with the opposition.

Ironically, the turmoil appears in one way to have been a boost to U.S. efforts to fight al-Qaida in Yemen, considered the terror network’s most active and dangerous branch.

Saleh seems to have sought to cling to power by making himself more valuable to Washington, which has pressed him to retire and allow a stable transition. In recent months, Saleh — long criticized as unreliable in his fight against al-Qaida — has given U.S. counterterrorism units a far freer hand to act in his country, U.S. and Yemeni officials say.

Top U.S. counterterrorism adviser John Brennan has said the Yemenis have been more willing to share information about the location of al-Qaida targets. Yemeni security officials say the U.S. was conducting multiple airstrikes a day in the south since May and that U.S. officials were finally allowed to interrogate al-Qaida suspects, something Saleh had long resisted. The officials spokes on condition of anonymity to discuss intelligence issues.

The cooperation was key to hunting down Anwar al-Awlaki, the American-Yemeni cleric who was killed in Friday’s strike by U.S. drones in a desert stretch of central Yemen. Killed with him was Samir Khan, a Pakistani-American who was a propagandist for the group, producing its English-language Web magazine, Inspire.

Also believed to have died in the blast is the top bombmaker for al-Qaida in Yemen — Ibrahim al-Asiri. The 29-year-old Saudi designed the explosives used in the group’s most notorious plots, including the Christmas 2009 failed attempt to blow up a jetliner headed to Detroit and an intercepted pair of explosives-laden printers that were mailed from Yemen to the United States in 2010.

Late Friday, two U.S. officials said intelligence indicated al-Asiri was among those killed in the strike. The officials spoke on condition of anonymity because al-Asiri’s death has not officially been confirmed.

Their deaths would strike a heavy blow to the international reach of al-Qaida in the Arabian Peninsula, as the group is called, since al-Awlaki was a valuable recruiter of Muslims abroad to carry out attacks and al-Asiri was an experienced constructor of explosives for such attacks.

But the strike “doesn’t change the dangerous dynamic. The big picture is that the country is falling apart,” said Bruce Riedel, a Brookings senior fellow and former CIA officer. “Saleh is pushing it into civil war by refusing to step down … creating the chaos that al-Qaida will thrive in.”

The Obama administration issued a travel alert on Saturday warning that al-Awlaki’s killing has raised the risk of anti-American violence worldwide.

Still at large are crucial figures in the group, including its leader Nasser al-Wahishi, a Yemeni who once served as Osama bin Laden’s personal aide in Afghanistan. He fled to Iran after the U.S.-led invasion of Afghanistan in 2001, and Tehran handed him over to Yemen, where he was jailed.

But in 2006, he broke out of a Sanaa prison along with nearly two dozen other al-Qaida militants in an escape U.S. officials have said had help from supporters within the regime.

He then founded al-Qaida in the Arabian Peninsula, incorporating remnants of the Saudi branch of the terror network that had been crushed by a crackdown in the kingdom in the mid-2000s, and launched a campaign to overthrow Saleh.

Alongside him is Qassim al-Raimi, the group’s military commander who Yemeni officials believe masterminded the Christmas airliner and the package bomb plots, and deputy leader Saeed al-Shihri, a Saudi who fought in Afghanistan and spent six years in the U.S. military prison at Guantanamo Bay, before being released and going through Saudi Arabia’s famous “rehabilitation” institutes.