With US officials and their allies scrambling to find ways to contain an increasingly belligerent Pyongyang, the US president will address the UN General Assembly on Tuesday and then confer Thursday with his Japanese and South Korean counterparts on the sidelines of the meeting.
Trump and South Korean President Moon Jae-In spoke by phone Saturday night and pledged "stronger pressure" on Kim Jong-Un's regime, the South's presidential office said, adding that the North must be made to realize that "further provocation" would put it on a "path of collapse."
The Security Council last Monday imposed a new raft of sanctions on North Korea -- but their impact depends largely on whether China, Pyongyang's ally and main economic partner, will fully implement them and on Russia, which is hosting tens of thousands of North Korean workers.
Washington's ambassador to the United Nations, Nikki Haley, kept up the rhetorical pressure ahead of the upcoming meetings in New York, asserting that if the North should pose a serious threat to the US or its allies, "North Korea will be destroyed."
Trump's earlier warning he would rain "fire and fury" on a recalcitrant North Korea, she said, was "not an empty threat."
"None of us want war," Haley added in an interview on CNN. "We wanted to be responsible and go to all diplomatic means to get their attention first. If that doesn't work, General Mattis" -- the US defense secretary -- "will take care of it."
As the US and its allies emphasise the diplomatic track, South Korea is also deploying a state-of-the-art US missile defense system. In their latest call, the White House said Trump and Moon had committed to "take steps to strengthen deterrence and defense capabilities" of South Korea, offering no details of how it might do so.
Analysts say that in the event of hostilities, millions of people in the Seoul area -- as well as the 30,000 US troops in South Korea -- would be vulnerable to attack by the thousands of artillery pieces the North has positioned near the border, with potentially staggering casualties.
The North's latest show of resistance came when it launched a long-range missile over Japan on Friday, just four days after the UN Security Council had passed a tough new package of sanctions.
At the request of the United States, the Security Council will hold a ministerial-level meeting Thursday on ways to enforce the latest sanctions, which include an export ban on textiles, freezing work permits to North Korean guest workers and capping oil supplies.
Haley said sanctions had already provided a "punch in the gut" to Pyongyang but that strict enforcement was crucial.
Separately, Trump's national security advisor, H.R. McMaster, agreed that "the critical thing is going to be to get all countries, every one, to do all they can to enforce those sanctions, to do everything they can, short of a military conflict, to resolve this problem."
But if diplomacy and economic pressure fail, he added, "We have to prepare all options."