SEOUL, South Korea — The clock is ticking.

Kim Jong-un, North Korea’s leader, has said that the United States has until the end of the year to make a new proposal to create a breakthrough in stalled negotiations on denuclearizing the Korean Peninsula.

The looming deadline — which North Korea has issued repeated warnings about — carries the implicit threat that the country could return to its alarming behavior of the past by ending its self-imposed moratorium on nuclear tests and launching long-range missiles capable of hitting American cities. On Thursday, it launched two short-range rockets, its 13th rocket or missile test since May.

“Today, we sit on top of a live volcano,” said Robert L. Carlin, a former nuclear negotiator at the State Department and longtime North Korea observer, describing a rapidly deteriorating situation on the peninsula during a lecture this month at Yonsei University in Seoul, the South Korean capital. “We don’t have a lot of time to back away.”