In Pakistan, the United States has struck at Al Qaeda in part through “signature” strikes — those that are aimed at killing clusters of people whose identities are not known, but who are deemed likely members of a militant group based on patterns like training in terrorist camps. The dispute over targeting could affect whether that tactic might someday be used in Yemen and Somalia, too.

The Defense Department’s general counsel, Jeh C. Johnson, has argued that the United States could significantly widen its targeting, officials said. His view, they explained, is that if a group has aligned itself with Al Qaeda against Americans, the United States can take aim at any of its combatants, especially in a country that is unable or unwilling to suppress them.

The State Department’s top lawyer, Harold H. Koh, has agreed that the armed conflict with Al Qaeda is not limited to the battlefield theater of Afghanistan and adjoining parts of Pakistan. But, officials say, he has also contended that international law imposes additional constraints on the use of force elsewhere. To kill people elsewhere, he has said, the United States must be able to justify the act as necessary for its self-defense — meaning it should focus only on individuals plotting to attack the United States.

The fate of detainees at Guantánamo Bay, Cuba, hangs heavily over the targeting debate, officials said. In several habeas corpus lawsuits, judges have approved the detention of Qaeda suspects who were captured far from the Afghan battlefield, as well as detainees who were deemed members of a force that was merely “associated” with Al Qaeda. One part of the dispute is the extent to which rulings about detention are relevant to the targeting law.

Congress, too, may influence the outcome of the debate. It is considering, as part of a pending defense bill, a new authorization to use military force against Al Qaeda and its associates. A version of the provision proposed by the House Armed Forces Committee would establish an expansive standard for the categories of groups that the United States may single out for military action, potentially making it easier for the United States to kill large numbers of low-level militants in places like Somalia.

In an interview, Senator Lindsey Graham, a South Carolina Republican on the Armed Services Committee, said that he supported the House version and that he would go further. He said he would offer an amendment that would explicitly authorize the use of force against a list of specific groups including the Shabab, as well as set up a mechanism to add further groups to the list if they take certain “overt acts.”

“This is a worldwide conflict without borders,” Mr. Graham argued. “Restricting the definition of the battlefield and restricting the definition of the enemy allows the enemy to regenerate and doesn’t deter people who are on the fence.”