SEOUL, South Korea — North Korea will not dismantle its nuclear weapons program until the United States also agrees to diminish its military capacity in the vicinity of the Korean Peninsula, its official news agency said on Thursday, clarifying a position that had remained vague since the leaders of both countries met in June.

At that meeting, President Trump and Kim Jong-un, the leader of North Korea, committed to work toward the “complete denuclearization of the Korean Peninsula.” But diverging interpretations of exactly what “complete” and “denuclearization” mean have led to a diplomatic stalemate and a breakdown in talks.

“When we refer to the ‘denuclearization of the Korean Peninsula,’ it means the removal of all sources of nuclear threat not only from the North and the South but also from all neighboring areas targeting the peninsula,” the official Korean Central News Agency said in a published commentary on Thursday. “The denuclearization of the Korean Peninsula should be defined as ‘completely eliminating the U.S. nuclear threat to Korea’ before it can eliminate our nuclear deterrent.”

North Korea has for decades maintained that it would not eliminate its weapons program until the United States closed its regional “nuclear umbrella,” a network of nuclear-capable submarines and bombers operating off the coasts of South Korea and Japan.