Liberal President Moon took office in May with a five-year single term as he vowed to seek sanctions and dialogue in resolving North Korea's nuclear standoff.
"The two leaders noted that North Korea continues to defy the global community, even after the United Nations strongly condemned North Korea?s repeated provocations twice in the past week", the White House said.
"None of us want war", Haley added in an interview on CNN.
Saying it is "very, very important" that President Trump will be highlighting the United Nations reform issue, Haley said: "We've got a massive reform package being led by the Secretary-General (Antonio Guterres) that really streamlines not just the processes, but also the budget as it goes forward, and makes the United Nations much more effective".
While at times North Korea evidences a poor understanding of how the USA government works-such as its 2014 demands that the Barack Obama administration prevent the film The Interview, starring Seth Rogan and James Franco, from airing-the Reconnaissance General Bureau has been analyzing US executives since the Korean War and surely has a good grasp on presidential powers and the role of the national security adviser.
The U.S. soldiers are conducting a joint exercise with their South Korean allies, and the mission for the day is to recapture a village in enemy hands.
"I believe you may have held great concerns and worries due to North Korea's repeated missile provocations and nuclear test that took place recently", the South Korean leader said while meeting with a group of South Korean residents and expatriates here.
It is just one of several that major world powers are engaged in on, over and near the Korean peninsula, amid heightened tension in the wake of North Korea's increasingly frequent missile tests and its sixth nuclear test this month.
The UNSC unanimously adopted an additional resolution on North Korea early last week to punish it for its latest and apparently most powerful nuclear test staged so far.
Haley said sanctions had already provided a "punch in the gut" to Pyongyang but that strict enforcement was crucial.
Pyongyang, an insular country with few outside contacts, says it needs nuclear weapons to protect itself from "hostile" United States forces and is determined to build the capacity to deliver a nuclear warhead that could hit the U.S. mainland.
The U.S. ambassador to the U.N., Nikki Haley, was at the White House briefing Friday afternoon.
As his administration continued its efforts to rein in the North, Trump himself gave a more unbridled account of his latest diplomatic contacts.