SAN’A, 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 Persian Gulf and lies on strategic sea routes leading to the Suez Canal.

But order has crumbled after more than seven months of protests demanding an end to President Ali Abdullah Saleh’s 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 United States has conducted 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 spoke 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 the desert 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.

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.”