At a news conference in the Philippines on Monday afternoon, President Obama initially scoffed when a reporter asked him to explain the “Obama doctrine” in light of his handling of recent world events.

But then he seemed to embrace the idea. Surveying hot spots from Syria to Ukraine, Obama laid out an incremental, dogged approach to foreign relations that relies on the United States deploying every possible economic and institutional lever before resorting to armed force.

“That may not always be sexy. That may not always attract a lot of attention, and it doesn’t make for good argument on Sunday morning shows,” said Obama, who is nearing the end of a week-long, four-nation tour of Asia. “But it avoids errors. You hit singles, you hit doubles; every once in a while we may be able to hit a home run. But we steadily advance the interests of the American people and our partnership with folks around the world.”

The passion in Obama’s delivery — he admitted he had gotten “all worked up” — underlined the quandary the White House now faces. With an array of unpalatable options around the globe, Obama and his aides are convinced that a cautious approach is helping the country avoid dangerous overseas entanglements while producing modest successes. But they are also increasingly frustrated with critics on Capitol Hill and in the media who have questioned why the president has been so reluctant to intervene abroad.

“Typically, criticism of our foreign policy has been directed at the failure to use military force,” Obama said. “And the question I think I would have is, why is it that everybody is so eager to use military force after we’ve just gone through a decade of war at enormous costs to our troops and to our budget?”

He added later: “We don’t [take action] because somebody sitting in an office in Washington or New York thinks it would somehow look strong.”

But Nile Gardiner, director of the Margaret Thatcher Center for Freedom at the conservative Heritage Foundation, said that Obama’s “track record, as a foreign policy president, has been an exceedingly poor one, despite the spin put on it by the president in Asia.”

“This is not a president who has projected strong U.S. leadership on the world stage or powerful engagement with key American allies,” Gardiner said, adding that “foreign policy often seems to be an afterthought” for Obama.

The past week highlighted some of the downsides to the administration’s strategy, as the Mideast peace process ran aground and Russian President Vladimir Putin showed no interest in bringing a peaceful end to the standoff in Ukraine between pro-Russian separatists and the government in Kiev.

But it also showed some of the possibilities, administration aides said. The Malaysian government signed on to the Proliferation Security Initiative, a global effort aimed at curbing the trafficking of weapons of mass destruction, which it had resisted embracing for more than a decade. The Philippine government agreed to a 10-year deal giving U.S. naval and air forces the most access to its waters since 1992. And Japan’s prime minister, Shinzo Abe, said he was confident that the United States could help establish a rules-based order that would keep China or any other powerful nation from violating the territorial claims of other countries.

“We want to make this a peaceful region which values laws, and in doing this, strengthening of our bilateral alliance is extremely important,” Abe said. “On this point, I fully trust President Obama.”

All four of the Asian leaders who met with Obama over the past week made clear that they not only appreciated his visit but saw their economic and security fortunes as tied to the United States. At a time when China’s expansionist efforts have alarmed some of its neighbors, the president’s emphasis on the importance of the rule of law and international arbitration pleased not just long-standing allies such as the Philippines but newer ones such as Malaysia.

“We are closer now than ever before,” said Malaysian Prime Minister Najib Razak.

Jonathan D. Pollack, a senior fellow in the John L. Thornton China Center at the Brookings Institution, wrote in an e-mail that the defense agreement with the Philippines signed Monday embodies Obama’s approach: aiming for greater U.S. flexibility in the region without provoking China.

“It is very much in the spirit of the administration’s foreign policy as a whole, signaling commitment without overt intervention,” he wrote. “The operative test in Asia is whether (unlike in Syria and in Ukraine) it inhibits rather emboldens others.”

In the case of Ukraine, administration officials said they are convinced that they can pressure Russia more effectively if any sanctions are coordinated with Europe and the other members of the G-7 — even if that means delaying sanctions on sectors of Russia’s economy.

In Manila on Monday, Obama questioned why some politicians and pundits are so quick to see military intervention as a simple solution for Ukraine and other conflicts.

“The point is that for some reason, many who were proponents of what I consider to be a disastrous decision to go into Iraq haven’t really learned the lesson of the last decade, and they keep on just playing the same note over and over again,” he said.

On other foreign policy questions — such as the war in Syria and the push to contain Iran’s and North Korea’s nuclear capabilities — the president said he continues to believe that his administration’s cautious efforts to keep these situations in check are America’s only logical option. He said early in his trip that 87 percent of the Syrian government’s chemical weapons cache has been turned over to international authorities.

Still, it’s unclear if Obama’s approach will be enough to reassure South Korean President Park Geun-hye, who warned Friday during a joint news conference in Seoul that the prospect of North Korea’s enhanced nuclear capability “is not going to be a problem only for the northeast Asia region. This is going to be a serious threat to global peace.”

For his part, Obama offered little comfort, saying that when it comes to North Korea, “we are not going to find a magic bullet that solves this problem overnight. What we’re going to have to do is to continue with a consistent, steady approach.”

Andrew Kuchins, director of the Russia and Eurasia Program at the Center for Strategic and International Studies, said his overarching concern about Obama’s foreign policy has been that the president and his national security team “have often been late” to the issues.

From Putin’s move into Crimea to Edward Snowden’s national security disclosures, Kuchins said, Obama has been “surprised more often than he should” — evidence that his interest in foreign policy is secondary.

In an unusually philosophical question-and-answer exchange with young Southeast Asian leaders in Kuala Lumpur, Malaysia, on Sunday, the president made clear that he recognized there are limits to what he can accomplish during his remaining time in office.

“Sometimes our efforts have been successful; sometimes . . . my efforts initially haven’t been as successful and I’ve had to keep on trying,” Obama said. “And I am confident that when I’m done as president, there’s still going to be parts of the world that are having war, that are having conflict, that are oppressing their own people. So I’m not going to solve all these problems. I’ve got to leave some work for all of you.”

Scott Wilson in Washington contributed to this report.