SEOUL — Pressure for South Korea to “go nuclear” — to develop its own warheads — is rising here in the face of shrill new challenges from North Korea and grave doubts about Washington’s commitment to defend the South under the next administration.

Demands for a nuclear South Korea are gaining momentum as North Korean leader Kim Jong-un boasts of his “policy on building the nuclear armed forces” and “increasing the number of nuclear weapons by geometrical progression.”

Long a simmering issue, the notion of the South rivaling the North as a nuclear power appeared as more than an abstract fantasy after Mr. Kim poured fuel onto the flames with a fire-eating speech on the 76th anniversary of the founding of the “Democratic People’s Republic of Korea” on September 10, 1948.

Pyongyang’s Korean Central News Agency quoted Mr. Kim as saying “the nuclear force of the DPRK and the posture capable of properly using it…should be more thoroughly perfected.”

Mr. Kim laid down a direct challenge to America’s strength in the region, blaming “the reckless expansion” of an American-led “nuclear-based military bloc” for having “come close to us as a grave threat,” KCNA reported. “Such actual threats will inevitably bring about more various threats,” requiring “more important measures … to maintain and further boost military supremacy.”

The prospect of North Korea increasing the North’s nuclear strength, after having recently agreed on a new military alliance with President Putin, raised the question of whether South Korea’s president, Yoon Suk-yeol, would stick to his decision not to order production of nuclear warheads under the aegis of the Korea Atomic Energy Institute.

After years of producing nuclear energy reactors for power plants, South Korea presumably could quite quickly match North Korea as a nuclear weapons power. Washington, however, has long opposed South Korea’s going nuclear — the phrase for making nuclear warheads as opposed to nuclear reactors for electrical power — while guaranteeing the “nuclear umbrella”needed for any contingency.

For now, “the Korean government has decided not to arm with nuclear capability,” said a research fellow with the Institute for National Security Strategy, Kim Jong-won, citing the officially stated position. “The controversy remains. It’s a very tough decision. The discussion is not over. Much depends on the further actions of North Korea.”

Much also depends on the policies of the next American president. President Trump’s talk of renewing his relationship with Mr. Kim has definitely played into calls here for South Korea to build its own nuclear defenses.

“We are looking for ways to assure the alliance will develop constructively,” said the president of INSS, Han Suk-hee, speaking at the Seoul Foreign Correspondents’ Club. “We recognize that South Korean security is no longer confined to traditional strategy.”  

Mr. Yoon faces strong opposition from conservatives within his ruling People Power Party demanding South Korea either develop its own nukes or reach a deal for Washington to base nukes on Korean soil as it did until then President George H.W. Bush withdrew them in 1991.

“There’s increasing movement that South Korea should have nuclear weapons,” said Mr. Han. 

The deepest fear is that Mr. Trump would make good on the idea he expressed during his first presidency of scaling back American forces, now totaling 28,500 troops in Korea, mostly soldiers and airmen.“He is an unpredictable man,” said the director of North Korean Studies at INSS, Byun Sang-jung, citing that factor as the overriding reason for “the increasing movement that South Korea should have nuclear weapons.”