Ms. Park’s difficulties have much to do with South Korea’s fractured domestic politics, in which liberal and conservative parties have often seized on North Korea as a way to discredit one another.

When progressives were in power from 1998 to 2008, they provided the North with massive shipments of aid, and engaged in investment and trade, betting that such actions would draw Pyongyang out of its hostile posture — what was known as the “sunshine policy.”

That decade of engagement slowed North Korea’s nuclear pursuits for a time, but did not stop them — the North conducted its first nuclear test in 2006. Ms. Park’s conservative predecessor, Lee Myung-bak, who took office in 2008, reversed course, curtailing aid and trade with the North, punishing it with tougher sanctions and refusing to negotiate until it committed to denuclearizing.

Ms. Park, 64, who became president in 2013, went farther down that path. The prevailing argument in Seoul and Washington — wishful thinking, critics say — was that the North would eventually buckle under economic pressure, or perhaps even implode under the untested leadership of Kim Jong-un, the young leader who came to power in late 2011. After Pyongyang’s fourth nuclear test in January, Ms. Park cut the Koreas’ last remaining economic tie: a jointly run industrial park in the border town of Kaesong.

But the North’s nuclear program has only accelerated in recent years. Three of the North’s five nuclear tests have taken place under Mr. Kim, during whose rule the North has tested 31 ballistic missiles, twice as many as it did during the 17 years that his father, Kim Jong-il, was in power. This year alone, the North test-launched 24 ballistic missiles. On Sunday, Yun Byung-se, South Korea’s foreign minister, acknowledged that North Korea was “at the final stage of nuclear weaponization.”

The North’s missile threat was Ms. Park’s justification for accepting the deployment of an American missile-interceptor battery, known as Thaad (for Terminal High Altitude Area Defense), on South Korean soil, a proposal that had been discussed with Washington for years. But that decision angered China — North Korea’s sole major ally, whose cooperation is crucial for enforcing sanctions — which sees Thaad as part of an American effort to encircle it.