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The Obama administration said Wednesday that al Qaeda and its acolytes—including radicalized Americans—remained the “preeminent security threat to the United States” even after the death last month of Osama bin Laden.

In its first formal document on counterterrorism strategy, the administration said direct attacks on the homeland by foreigners or homegrown militants were its top priority, ahead of such militant-heavy regions as Yemen and the Afghanistan-Pakistan border.

“We seek nothing less than the utter destruction of this evil that calls itself al Qaeda,” John Brennan, the president’s chief counterterrorism adviser, said in a speech Wednesday.

Rather than marking a shift in strategy, the document formalizes the approach to fighting terrorism that the administration has taken since President Barack Obama came to office in 2009, and continues many elements used by his predecessor, George W. Bush.

The document’s release comes amid upheaval in the Middle East and North Africa, which has blurred the battle lines between the U.S. and militant Islamists. Peaceful protests in countries such as Egypt and Tunisia have toppled long-standing repressive governments and undermined al Qaeda’s message of change through violence. Al Qaeda was further weakened by the Navy SEAL team assault that killed bin Laden in his Pakistan hideout.

However, administration officials say the turmoil also provides opportunities for the al Qaeda network to carve out new havens and prepare fresh attacks.

Mr. Brennan said the administration would continue “targeted, surgical” strikes to eliminate al Qaeda leaders and boost cooperation with other countries, including Yemen, where a longtime U.S. ally, Ali Abdullah Saleh, has a precarious hold on power, and Pakistan, whose often-fragile relations with the U.S. have become even more uncertain since bin Laden’s presence there was revealed.

“As frustrating as this relationship can sometimes be, Pakistan has been critical to many of our most significant successes against al Qaeda,” Mr. Brennan said in prepared remarks. “I am confident that Pakistan will remain one of our most important counterterrorism partners.”

The administration’s plan also emphasizes steps to beef up homeland security—especially resilience to cyber or biological attack—and stresses the need to counter al Qaeda on the ideological front.

For the past two years, undermining al Qaeda’s ability to attract new recruits, especially inside the U.S., has been part of the administration’s counterterror approach. Mr. Brennan singled out two American-born, English-speaking spokesmen for al Qaeda, Adam Gadahn in the Pakistan-Afghanistan region and Anwar al Awlaki in Yemen, for their roles in radicalizing recruits.

“This is the first counterterrorism strategy that focuses on the ability of al Qaeda and its network to inspire people in the United States to attack us from within,” Mr. Brennan said.

Foiled plots led by homegrown radicals include a 2009 plan to blow up New York City subways; a 2010 plan to explode a car bomb in Times Square; and numerous “lone-wolf” plans to blow up prominent buildings that were foiled by FBI sting operations.

Mr. Brennan said that this summer the administration would present a more detailed plan to work with local Muslim and Arab communities to counter violent extremism in the U.S.

Write to Keith Johnson at keith.johnson@wsj.com