Mr. Trump is giving the Pentagon and the C.I.A. broader latitude to pursue counterterrorism drone strikes and commando raids away from traditional battlefields. Two government officials said Mr. Trump had recently signed his new rules for such kill-or-capture counterterrorism operations, without major changes to an interagency agreement first described last month by The New York Times.

Under the Obama-era rules, there was individualized high-level vetting of proposed strikes, and targets had to pose a specific threat, as individuals, to Americans. Under the new Trump rules, the administration will instead approve a “persistent campaign of direct action” for various countries where Islamist militants are operating, without higher-level review of particular strikes, and targets may include any suspected member of a group deemed covered by the 9/11 war authorization.

And while the Trump administration decided to keep an Obama-era requirement of “near certainty” that no civilians would be killed, it reduced the required level of confidence that the intended target was present in a strike zone from “near certainty” to “reasonable certainty,” one official said — further lowering constraints on attacks.

Moreover, NBC News reported this past week that the Trump administration was exploring arming the surveillance drones that now fly over Niger and Mali in search of suspected Islamist militants. The new rules could also permit the Pentagon to carry out offensive ground combat operations in North and West Africa, escalating deployments that key lawmakers seem to have been only dimly aware of before the deaths of the four soldiers this month.

“I didn’t know there was a thousand troops in Niger,” Senator Lindsey Graham, a South Carolina Republican on the Senate Armed Services Committee, recently told NBC’s “Meet the Press.” Mr. Graham opposes rewriting the 9/11 war authorization law but wanted more information about what the government is doing with it, saying: “This is an endless war without boundaries, no limitation on time and geography. You got to tell us more.”

The questions about Mr. Trump’s interpretation of his war powers range beyond conventional counterterrorism operations.