Ever since the Korean War was halted in an uneasy truce in 1953, South Koreans have lived under an American promise to defend their country, if necessary, with nuclear weapons. President Biden emphatically reiterated that commitment last year, vowing that any nuclear attack by North Korea would lead to the destruction of its government.

But decades of American assurances have failed to deter North Korea from building a nuclear arsenal and then expanding it. Led by Kim Jong-un, North Korea has also become more provocative, testing missiles powerful enough to reach the United States. And it has rattled South Korea by reviving a Cold War-era defense agreement with Russia, another nuclear-armed state.

The South has long considered it a taboo to pursue atomic weapons in defiance of Washington’s nonproliferation policy. But jitters about security here have been intensified by the possible re-election of former President Donald J. Trump, whose commitment to the alliance between Washington and Seoul appears to be shaky at best.

Now, a growing majority of South Koreans say their country needs its own nuclear weapons instead of relying on the United States for protection. The idea, although still disavowed by the South Korean government, is increasingly becoming part of mainstream political debate.

Polls show that many South Koreans say they can no longer trust the American nuclear umbrella to guard them from North Korea. They doubt that Washington would come to their aid in the event of a conflict with North Korea now that Pyongyang is racing to develop the ability to attack American cities with nuclear warheads.