WASHINGTON — When the two pirates boarded the U.S.S. Sterett off the coast of Somalia on Monday, American officials thought they were headed for a breakthrough in the four-day standoff with a gang that had seized four Americans vacationing on their 58-foot yacht.

But an F.B.I. hostage-rescue negotiator aboard the Sterett came to believe the two Somalis were not serious. So the Americans took them into custody and told the pirates back on the yacht to send over someone they could do business with.

What happened next is sharply contested and raises questions about the crucial decision to detain the pirate leaders.

American officials said the pirates on the yacht, called the Quest, seemed relieved — even “exceptionally calm” — when told their senior commander was cooling his heels in a Navy brig.