WASHINGTON — President Obama and his legal advisers are deliberating about how the United States military may lawfully continue participating in NATO’s bombing campaign in Libya after next week, when the air war will reach a legal deadline for terminating combat operations that have not been authorized by Congress.

Under the War Powers Resolution of 1973, a president must terminate such operations 60 days after he has formally notified lawmakers about the introduction of armed forces into actual or imminent hostilities. The Libya campaign will reach that mark on May 20.

Though Congressional leaders have shown little interest in enforcing the resolution, James Steinberg, the deputy secretary of state, was asked Thursday about the deadline at a Senate Foreign Relations Committee hearing.

He said the administration was examining the military’s “role and activities as we move through the next period of time” and would consult Congress about evaluating “what we think we can and can’t do.”