SEOUL, South Korea — North Korea announced plans on Tuesday to restart a mothballed nuclear reactor, the latest in a series of provocations by its leader, Kim Jong-un, to elicit a muted response from American officials, who believe they can wait out Mr. Kim’s threats until he realizes his belligerent behavior will not force South Korea or the United States into making any concessions.

“Right now, they’re testing the proposition that we’ll choose peace and quiet, and put it on our MasterCard,” said a senior American official, who spoke on the condition of anonymity to discuss the administration’s internal calculations. “When they get through this cycle, they will have gotten no return on their investment.”

Secretary of State John Kerry, using time-tested diplomatic language, said North Korea’s plan to restart the reactor would be a “provocative act” and “a direct violation of their international obligations.” Speaking in Washington after his first meeting with South Korea’s foreign minister, Yun Byung-se, Mr. Kerry reaffirmed the determination of the United States to defend its ally.

American officials still worry about the consequences of any miscalculation, given the hair-trigger tensions on the Korean Peninsula and Mr. Kim’s inexperience at this type of brinkmanship. The top American commander in South Korea, Gen. James D. Thurman, called the situation “tense” and “volatile” in an interview with ABC News.