Trump and South Korean President Moon Jae-in are to meet in Seoul on Tuesday.

The meeting will come at a time of heightened tension over North Korea's pursuit of nuclear weapons and ballistic missiles capable of delivering them to the American mainland.

"The discussion will also be about what more can we do, what more can all countries do to resolve this short of war," McMaster added. "What we think is essential is to continue the diplomatic and economic isolation of the North Korean regime so that leaders within that regime recognize that this weapon, this pursuit of this destructive capability, is not making them more secure, it's making them less secure, and to conclude that it is in their interest to begin denuclearization."

Time is running out to deal with the North Korean threat, the adviser warned.

But he also made clear that the US has not given up on diplomacy.

"Diplomacy is our main effort now," he said, "but it's diplomacy with other countries who recognize the grave threat and who are working together."

McMaster said Trump has instructed officials to ask other countries to do more to isolate the North until the regime realizes it has no option but to denuclearize.

The U.N. Security Council unanimously adopted two sanctions resolutions against Pyongyang after its two long-range missile tests in July and its sixth and most powerful nuclear test in September.

They aim to starve the regime of the financial and energy resources it needs to develop its weapons programs.

The sanctions' effectiveness will largely hinge on cooperation from China, which is responsible for 90 percent of North Korea's external trade and the regime's only major ally.

The White House has said Trump will seek to secure China's commitments to exert more pressure on the North when he meets with Chinese President Xi Jinping in Beijing later next week.

McMaster said he welcomes this week's announcement that Seoul and Beijing have agreed to move forward despite a dispute over South Korea's hosting of the THAAD US missile defense system on its soil.

"What's important is that China is no longer punishing South Korea for defending itself, which I always thought didn't make any sense," he said, referring to Beijing's economic retaliation against Seoul.

"What China may be realizing as well is that it makes more sense, at least from our perspective, to prioritize its relationship with South Korea over its relationship with North Korea, which is not only a dangerous state but a failing state at the same time."

If North Korea continues to pursue nuclear weapons, McMaster said there could be a breakdown of the nonproliferation regime in Northeast Asia.

"And that's not in anybody's interest, right?" he said, apparently addressing growing calls in South Korea and Japan for their own nuclear armament.

Trump's 12-day swing through Asia will also include stops in Japan, Vietnam and the Philippines. It will be his first presidential trip to the region. (Yonhap)