A South Korean news magazine with front cover photos of U.S. President Donald Trump and North Korean leader Kim Jong Un, right, and a headline "Korean Peninsula Crisis" is displayed at the Dong-A Ilbo building in Seoul, South Korea, Sept. 11, 2017.
A South Korean news magazine with front cover photos of U.S. President Donald Trump and North Korean leader Kim Jong Un, right, and a headline "Korean Peninsula Crisis" is displayed at the Dong-A Ilbo building in Seoul, South Korea, Sept. 11, 2017.

WHITE HOUSE - On the eve of President Donald Trump's trip to Asia, the White House said Thursday that the threat from Pyongyang would be at the top of his agenda in his meetings with leaders and that denuclearization of North Korea was the only acceptable outcome.

WATCH: Trump on visiting Asia

If this is not achieved through pressure by economic sanctions and diplomacy, national security adviser General H.R. McMaster warned, the United States "will respond with all capabilities available to North Korean aggression."

Recent polls by NBC News/SurveyMonkey and Economist/YouGov show Americans consider North Korea to be the most immediate threat to the United States.

Trump is scheduled to visit South Korea, the North's rival, on November 7-8. It will be the second stop of his 12-day trip to five countries.

The president's talks with South Korean President Moon Jae-in and other world leaders are to center on questions about how to deal with Pyongyang's development of nuclear weapons and ballistic missiles.

"Our goal is not war, but rather the complete, verifiable and irreversible denuclearization of the Korean Peninsula," said Defense Secretary Jim Mattis last Friday at the Demilitarized Zone between North and South Korea.

There is increasing anxiety on both sides of the Pacific about what Trump views as necessary to achieve his administration's vow to eliminate the threat to the United States posed by Pyongyang's weapons of mass destruction.

"I think we will come down to a point where — I liken it to a kind of a Cuban Missile Crisis — there's a finite time period where we have to make a decision, whether it's political or military, that really will change the political landscape of the Korean Peninsula," said Jae Ku, director of the U.S.-Korea Institute at the Johns Hopkins University's School of Advanced International Studies.

North Korean leader Kim Jong Un reacts during a ce
FILE - North Korean leader Kim Jong Un reacts during a celebration for nuclear scientists and engineers who contributed to a hydrogen bomb test, in this undated photo released by North Korea's Korean Central News Agency in Pyongyang, Sept. 10, 2017.

Highly charged rhetoric

The U.S. president and North Korean leader Kim Jong Un recently have had an unprecedented, highly charged exchange of rhetoric.

"The insults traded back and forth decrease the legitimacy of the United States and of the United States president," Thomas Countryman, former U.S. acting undersecretary for arms control and international security, told VOA. "It bothers me to see an American president sink to the same level of insults and threats that we have seen from the North Koreans over many years."

Asked whether Trump might tone down his "fire and fury" threat against North Korea during the trip, McMaster responded, "I don't think the president really modulates his language. Have you noticed him do that?"

The national security adviser said what's really inflammatory "is the North Korean regime and what they're doing to threaten the world."

Some in South Korea, including the main opposition conservative party, are pushing not only to have American tactical nuclear weapons brought back to the country but also for U.S. support to allow Seoul to possess its own nuclear arsenal.

"If the two countries push forward with redeploying tactical nuclear weapons, I'm certain it'll not only show the people of the two countries the solidarity of the alliance, but also prevent Kim Jong Un from having further desires to provoke," Liberty Korea Party Chairman Hong Joon-pyo said October 26 at the National Press Club in Washington.

Polls show 60 percent of South Koreans favor building nuclear weapons and nearly 70 percent want the reintroduction of American tactical nuclear weapons for battlefield use, which were withdrawn in 1991.

"You sense the anxiety, you sense the fear, you sense that this is something different that the Koreans are facing. And so, as a result, I think they have latched on to this idea that tactical nuclear weapons may provide that kind of security to them, and they haven't thought through all the messy issues that come with it," Ku, the U.S.-Korea Institute director, told VOA.

FILE - U.S. President Donald Trump walks with Sout
FILE - U.S. President Donald Trump walks with South Korean President Moon Jae-in to make statements in the Rose Garden at the White House in Washington, June 30, 2017.


South Korea's Moon is ruling this out.

"According to the joint agreement by the two Koreas on denuclearization, North Korea's nuclear state cannot be accepted or tolerated. We will not develop or possess nuclear weapons, either," Moon told the National Assembly in his state-of-the-nation address Wednesday.

Trump will address the National Assembly before flying from South Korea to Beijing. There, he will discuss the heightened tensions on the Korean Peninsula with Chinese President Xi Jinping.

China is North Korea's only remaining significant ally. China has expressed frustration with its smaller but increasingly provocative neighbor, but Trump is expected to request that Beijing apply even more pressure on Kim Jong Un.

"China is definitely doing more, but obviously it's not enough," McMaster told reporters at the White House on Thursday.