SEOUL, South Korea — Secretary of State John Kerry rebuffed North Korea’s demand that the United States and South Korea briefly delay a joint military exercise this month so that it does not coincide with the scheduled reunion of families separated by the Korean War.

If held, the reunions would signal a significant thaw between the two Koreas. North Korea argues that exercises raise tensions, while American and South Korean officials view Pyongyang’s latest demand as part of its longstanding effort to undermine the United States’ military commitment to South Korea.

Mr. Kerry’s comments came during the first stop of a multination trip to Asia meant in part to solidify efforts for dealing with North Korea and its increasingly sophisticated nuclear weapons programs. His arrival in South Korea came on the heels of a White House announcement on Wednesday that President Obama will visit South Korea, Japan, Malaysia and the Philippines in April, part of the administration’s continuing efforts to direct more of its attention to Asia as China rises.

The joint military drills with South Korea are supposed to begin on Feb. 24. In a news conference with his South Korean counterpart, Mr. Kerry said that it was not “appropriate” to link humanitarian issues with North Korea’s security demands.