The most recent episode began after American officials tracked a North Korean cargo ship, the M/V Light, that was believed to have been involved in previous illegal shipments. Suspecting that it was carrying missile components, they dispatched a Navy vessel, the destroyer McCampbell, to track it.

“This case had an interesting wrinkle: the ship was North Korean, but it was flagged in Belize,” one American official said, meaning it was registered in that Central American nation, perhaps to throw off investigators.

But Belize is a member of the Proliferation Security Initiative, an effort begun by President George W. Bush’s administration to sign up countries around the world to interdict suspected unconventional weapons. It is an effort that, like the military and C.I.A. drone programs, Mr. Obama has adopted, and one of the rare areas where he has praised his predecessor.

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According to American officials, the authorities in Belize gave permission to the United States to inspect the ship.

On May 26, somewhere south of Shanghai, the McCampbell caught up with the cargo ship and hailed it, asking to board the vessel under the authority given by Belize. Four times, the North Koreans refused.

As in the 2009 case, which involved the North Korean vessel the Kong Nam 1, the White House was unwilling to forcibly board the ship in international waters, fearing a possible firefight and, in the words of one official, a spark “that could ignite the Korean peninsula.” Moreover, the Americans did not have definitive proof of what was in the containers — and a mistake would have been embarrassing.

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“There is always a chance that the North is setting us up for a raid that they know will find nothing,” one official said. “So we want to make sure we don’t fall into a trap.”

By happenstance, a group of senior officials from the Association of Southeast Asian Nations — including a representative from Myanmar — was in Washington while the slow-speed chase was occurring 8,000 miles away. On May 27, when the group visited the Old Executive Office Building opposite the White House, Gary Samore, the president’s top nuclear adviser, addressed the officials, urging Vietnam, Thailand, Indonesia and Malaysia to fully join the nonproliferation effort.

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He then surprised the Asian officials by telling them he had a “sensitive subject” to raise, and described the American suspicions, providing the group with a picture of the ship on its way to Myanmar. He reminded them that under United Nations Security Council Resolution 1874, which was passed in response to the North Korean nuclear test in 2009, its vessels are to be inspected if “reasonable grounds” exist to suspect that weapons are being exported.

“The Burmese official in the room protested that we were making accusations,” said one American official familiar with the exchange. Myanmar, formerly known as Burma, has denied stockpiling missiles or buying parts from North Korea. It repeated those denials during recent visits to the country by a midlevel State Department official and by Senator John McCain.

American officials dismiss those denials, pointing to years of evidence of missile-related purchases during both the Bush and Obama administrations. But they concede they are mystified about Myanmar’s motives. The missiles that they believed were aboard the M/V Light have a range of about 350 miles, meaning they could hit parts of India, China, Thailand or Laos — all unlikely targets.

The message apparently got across. A few days later, long before approaching Myanmar, the cargo ship stopped dead in the water. Then it turned back to its home port, tracked by American surveillance planes and satellites, and suffering engine trouble along the way.