The United Nations Security Council was to meet at 3 p.m. EDT (1900 GMT) on Friday at the request of the United States and Japan, diplomats said, just days after the 15-member council unanimously stepped up sanctions against North Korea over its September 3 nuclear test.
They also came as world leaders begin arriving in NY for the annual meeting of the U.N. General Assembly this week, where North Korea will be high on the agenda.
The United States and South Korea are technically still at war with North Korea because the 1950-53 Korean conflict ended with a truce and not a peace treaty.
Trump spoke with Moon from his New Jersey golf club, where aides said he was spending the weekend preparing for his United Nations debut.
Haley, briefing reporters at the White House with National Security Advisor H.R. McMaster, said tough sanctions and further diplomatic methods are necessarily and being pursued.
White House press secretary Sarah Huckabee Sanders said Mr. Trump "is still 100 percent committed to the wall", after House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer said the president made a deal with them about the Deferred Action for Childhood Arrivals (DACA) program that excludes a border wall. He said at Joint Base Andrews near Washington that North Korea "has once again shown its utter contempt for its neighbors and for the entire world community".
Kim has threatened Guam, a USA territory in the Pacific, and has fired missiles over Japan, a U.S. ally.
"China supplies North Korea with most of its oil".
On Friday, the U.N. Security Council condemned North Korea's "highly provocative" test of an intermediate-range missile, which hurtled over USA ally Japan into the northern Pacific Ocean.
"I think it's a signal that the USA takes the General Assembly much less seriously than it did under President Obama", said Gowan.
Mr Trump, in a tweet, asserted that long lines for fuel were forming in North Korea, saying that was "too bad".
"We have pretty much exhausted all the things that we can do at the Security Council at this point", Haley told CNN's "State of the Union", adding that she was perfectly happy to hand the North Korea problem over to Defense Secretary James Mattis.
"For those who have said, and been commenting about a lack of a military option, there is a military option", McMaster said.
As a result, the United States has pressured China, North Korea's largest trading partner, to help quell North Korea's threats and missile tests by threatening economic penalties.
"But of course, this will nearly [certainly] figure in every conversation that leaders have here during the next week", a senior European diplomat said.
"We wanted to be responsible and go to all diplomatic means to get their attention first". But we also have to look at the fact that you are dealing with someone [in Kim] who is being reckless, irresponsible and is continuing to give threats not only to the United States, but to all of its allies. "... We've been kicking the can down the road and we're out of road". Mr. Trump tweeted that the, "sick and demented people" were "in the sights of Scotland Yard", prompting questions about whether Mr. Trump divulged sensitive or even classified information from an earlier call with British Prime Minister Theresa May.
At the same time, the administration signaled that it is not pursuing regime change, a position that could help persuade Beijing to play a stronger role in pressuring Kim. "The United Nations, of course, holds tremendous potential to realize its founding ideals, but only if it's run more efficiently and effectively", McMaster said.
Trump will meet with leaders from Europe, Asia, the Middle East and Latin America throughout the week, but his remarks, scheduled for Tuesday morning, will be the president's highest profile opportunity to explain his foreign policy vision couched in his "America first" agenda.
Asked about the test on Thursday, Trump said he's working with China to continue to exert more pressure on Pyongyang, but he declined to elaborate.
"What's different about this approach is, we're out of time", said McMaster.