Defense Secretary Lloyd J. Austin III said on Wednesday that fears of a wider regional war in the Middle East would probably subside once Israel transitioned its military mission in Gaza to lower-intensity combat operations.

Asked whether a decision by Israel to shift from high-intensity operations to more targeted, intelligence-driven missions, as the Biden administration has repeatedly urged in recent days, could reduce the risk of broader conflict with Iran and its regional proxies, Mr. Austin indicated that it would help.

“If that happens, when that happens,” Mr. Austin said, “it’s logical that we would see some of that, you would see some reduction in activity.”

Mr. Austin did not elaborate on his comments, which were made in response to questions from reporters traveling with him aboard the aircraft carrier Gerald R. Ford. But other senior administration officials have said privately that the rising death toll in Gaza — now about 20,000 people, according to health officials there — is fueling the momentum of Iranian proxy attacks against Israel and its allies.