Mr. Obama and his senior staff members tell a very different story — one in which the president has capitalized on the benefits of getting out of Iraq, and almost out of Afghanistan, to employ more subtle, smarter tools of national power. The “pivot to Asia,” which has been slow to materialize, was supposed to be emblematic of a new combination of soft and hard power; it was as much about building trade relationships as making it clear to the Chinese leadership that America has no intention of ceding the East and South China Seas as areas where Beijing could expect to become the sole power.

The latest budget invests more in drones and cyber and Special Operations forces, and pares back on conventional troops and the equipment for long land wars.

“If we are constantly overextending ourselves, chasing every crisis, we’re not going to be able to play the long game required for American primacy,” said Benjamin J. Rhodes, a deputy national security adviser.

Mr. Obama insists he is sending the right signals: He argued to Jeffrey Goldberg in Bloomberg View recently that there are “35,000 U.S. military personnel” in the Middle East who are constantly training “under the direction of a president who already has shown himself willing to take military action in the past.”

But the president also made the case that Washington is awash with muscle-flexing by those who have not learned the lessons of the past decade. If he had sent troops to Syria, Mr. Obama argued, “there was the possibility that we would have made the situation worse rather than better on the ground, precisely because of U.S. involvement, which would have meant that we would have had the third or, if you count Libya, the fourth war in a Muslim country in the span of a decade.”

Still, some senior officials who left the White House after the first term concede — when assured of anonymity — that Mr. Obama erred in failing to have a plan to back up his declaration that President Bashar al-Assad had to leave office. And Arab leaders argue that Mr. Obama’s last-minute decision to pull back from the missile strike on Syria will embolden the Iranians as they decide how much, if any, of their nuclear program to give up.

Foreign leaders say they see America’s unwillingness to act as the inevitable backlash of too many years at war. “In the past decade we’ve seen the consequences and the limits of taking action,” said David Miliband, the former British foreign secretary who now runs the International Rescue Committee, as he described his organization’s efforts to help an overwhelming influx of refugees over Syria’s borders. “Here we’re seeing the consequences and limits of inaction.”