Recent satellite data shows continued work at the nuclear test site in North Korea, although experts analysing the data say that preparations do not appear to have progressed far enough for an imminent test.
Adding to tensions surrounding Obama's visit to South Korea, the North announced on Friday it had detained a 24-year-old American this month who demanded asylum after arriving in the country on a tourist visa.
Obama is using his week-long Asia tour to try to ease doubts among U.S. allies about his promise to "rebalance" military, diplomatic and economic resources toward the fast-growing Asia-Pacific region.
He has sought to strike a balance between showing the United States will be a counterweight to China without alienating Beijing, which worries that Washington wants to contain its growth and influence.
Obama and Park also urged China, North Korea's main ally, to uses itsinfluence to help rein in its unpredictable neighbor.
Underscoring the vast differences between the economically dynamic South and the impoverished North, Obama met earlier with a business roundtable in Seoul where he hailed the benefits of a U.S.-South Korea trade agreement that took effect in 2012.
Obama's visit came at a time when South Koreans remain preoccupied with the aftermath of the sinking of a ferry carrying hundreds of youngsters, one of the worst tragedies to hit the country in modern times.
Stressing a deep U.S. bond with South Korea during his visit, Obama has expressed condolences to Park and the Korean people. More than 300 people drowned or are missing and presumed dead after the April 16 sinking. Investigations are focused on human error and mechanical failure.
Before visiting Seoul, Obama spent three days in Tokyo - the first full state visit by a U.S. president since 1996 - on a visit meant to show that the U.S.-Japan alliance, the main pillar of America's security strategy in Asia, is solid at a time of rising tensions over growing Chinese assertiveness and the North Korean nuclear threats.
He is also visiting Malaysia and the Philippines.