A leading House Republican said Wednesday that he wants to require the U.S. military to “promptly” inform Congress about every drone strike it conducts outside Afghanistan as well as other military operations to kill or capture suspected terrorists outside declared war zones.

Rep. Mac Thornberry (Tex.), the chairman of a House Armed Services subcommittee, said his panel already receives regular reports on counterterrorism operations from the Defense Department. But he said he will introduce a bill Thursday that would codify the practice into law to reassure the public that Congress is providing adequate oversight of drone strikes and other sensitive military operations.

“We’ve been doing a lot of this oversight anyway,” Thornberry said in an interview. “But I think it is time, for a variety of reasons, to formalize that in statute and make it clear to the American people that it’s happening, because a lot of the oversight that has gone on, most people don’t know about it.”

After years of keeping largely quiet, some members of Congress have started to agitate for more transparency and legal justification from the Obama administration regarding drone strikes by the CIA and the military. Lawmakers have held several hearings on the subject in recent weeks, although no consensus has emerged on what changes are required.

Thornberry’s bill runs counter to the trend. He said he’s generally satisfied with the way the administration discloses secret military operations to the Armed Services Committee and covert CIA operations to the House Intelligence Committee, of which he is also a member.

The military, he said, briefs his subcommittee within “hours or days” after each drone strike and other “lethal targeting actions” outside Afghanistan. The Pentagon is supposed to do the same for operations that capture suspected terrorists or other individuals outside the war zone, although he acknowledged that there have been only a few cases in recent years.

In recent years, the Armed Forces subcommittee has modified the military’s reporting requirements to keep up with changes in the nature of warfare, he said. Two years ago, lawmakers passed a measure requiring the Defense Department to provide a formal quarterly briefing on counterterrorism operations. Last year, it did the same for cyber operations.

“There’s been a comfort level that’s been achieved and that’s even an additional reason to say, ‘Okay, we’ve got this down to where it’s working pretty well, so let’s put it in statute so everybody knows,’ ” he said.

Thornberry’s opinion matters because he leads the subcommittee that the Pentagon is supposed to brief about drone strikes and other sensitive operations. But he also has the backing of Armed Services Committee Chairman Buck McKeon (R-Calif.).

“This is consistent with the kind of oversight that the chairman wants to see,” said Claude Chafin, a committee spokesman.

Caitlin Hayden, a White House spokeswoman, declined to comment on Thornberry’s measure because it has not been introduced.

But she noted that President Obama has said he intends to “engage Congress to ensure not only that our targeting, detention and prosecution of terrorists remains consistent with our laws and system of checks and balances, but that our efforts are even more transparent to the American people and to the world.”

Thornberry’s bill would require the administration to produce a report describing its legal justification and decision-making processes for military drone strikes and other capture-or-kill operations outside Afghanistan. Although the administration has recently shared some of its legal rationale with lawmakers, it has done so reluctantly and behind closed doors.

Thornberry said he is fine with the secrecy and does not think the administration has been excessive in that regard.

“The reason to have this information classified is still there and very strong,” he said. “It’s really important that everyone maintains the close-hold nature of this information. You don’t want to tell the bad guys what you’re doing. You don’t want to endanger the lives of our folks who are out there keeping us safe.”