Trump went on, "Again, I want to just say and thank President Xi [Jinping] of China for the very bold move he made today. That was a somewhat unexpected move, and we appreciate it."
Trump spoke after signing an executive order aimed at companies and financial institutions that do business with North Korea.
"Foreign banks will face a clear choice to do business with the United States or facilitate trade with the lawless regime in North Korea," he said.
Trump argued that his order will "cut off sources of revenue that fund North Korea's efforts to develop the deadliest weapons known to humankind." Early this month, North Korea conducted its sixth and most powerful nuclear test yet, and last week the country fired a missile over Japanese airspace. Abe welcomed the new sanctions enforced by the United States.
According to Trump, the U.S. Treasury Department will begin identifying new industries that it can target with strong sanctions, like manufacturing, fishing and textiles.
"For much too long, North Korea has been allowed to abuse the international financial system to facilitate funding for nuclear weapons and missile programs," said Trump.
He said the U.S. seeks a "complete denuclearization of North Korea."
Treasury Secretary Steve Mnuchin affirmed the president's stance, telling reporters this afternoon, "No bank in any country should be used to facilitate Kim Jong Un's destructive behavior." He emphasized that "the action is directed at everyone" and not specifically China.
"The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea," Trump said Tuesday in his first address to the United Nations General Assembly.
"Rocket Man is on a suicide mission for himself and for his regime," Trump said, using an epithet he has recently adopted to refer to Kim.
Trump teased the announcement during his meeting with Moon earlier in the day and told reporters to "stay tuned."
During that meeting, Moon praised Trump's speech Thursday as "strong" and said he believes it will "help contain North Korea."
"North Korea has continued to make provocations, and this is extremely deplorable, and this has angered me and our people," Moon said. "The United States has responded firmly and in a very good way."
"I'm happy you used the word 'deplorable,'" Trump said, getting some laughs from the room. "I promise, I did not tell them to use that word."
"That's been a very lucky word for me and many millions of other people," he added, referring to Democratic presidential nominee Hillary Clinton's characterization of some of Trump’s supporters as “deplorable” before the election last year.