There are nearly 30,000 US troops permanently stationed in South Korea and 47,000 in Japan, with little appetite for nuclear weapons in either nation.
Asked to respond to Trump's 'America first' policy to wean nations off US support, South Korean Defence Ministry spokesman Moon Sang-Gyun said it would be inappropriate to comment on remarks by a US presidential candidate.
But he stressed there was no change to Seoul's position that the South Korea-US Mutual Defence Treaty remained the bedrock of the alliance with Washington.
Japan's top government spokesman Yoshihide Suga also declined to react directly to Trump's comments, published Saturday in the New York Times, but insisted the military alliance with Washington was crucial and enduring.
"It is the main pillar of Japan's foreign policy and extremely important for the prosperity and safety of the Asia-Pacific region and the world," Suga told reporters.
He said Japan would maintain its policies against nuclear possession and production, and a ban on foreign nuclear weapons on its territory.
Support for a nuclear-armed South Korea is a minority voice in the country -- although one that grows louder after every nuclear test by North Korea.
Japan is widely seen as having the know-how to produce nuclear arms but, as the only country to have suffered an atomic attack, public opinion is strongly opposed to such a move.
Trump's remarks caused a stir in the media, however, with Japan's mass-circulation Yomiuri Shimbun daily saying they had generated some government concern.
"If he becomes the US president, it would be a problem for the Japan-US national security system," it quoted an unnamed source close to the government as saying.
South Korean newspapers called Trump's comments dangerous and shocking.
In a strongly-worded editorial, the English-language JoongAng Daily said: "His views -- stemming from a critical lack of understanding about the alliance and security issues -- are utterly short-sighted.
"We are dumbfounded at such myopic views of a leading candidate," it said.
There are few takers in Washington for the idea of nuclear-armed Asian allies, which would set back a longstanding, if repeatedly violated, principle of not allowing new nations into the nuclear club.
Trump said a nuclear-armed South Korea and Japan could be preferable to the current situation in which both countries look to the US nuclear umbrella to counter the threat from North Korea and a rising China.
His foreign policy envisaged withdrawing US troops from the two Asian nations unless they significantly increased their contributions to Washington for maintaining that military presence.