Moon also noted the rapid advancement in the North's nuclear and missile capabilities, calling Pyongyang's latest missile launch a serious provocation that violates UN Security Council resolutions and poses serious challenges to global peace and stability.
Han said that Sunday's test-launch was "successful in flight".
The envoy replied that such remarks were a part of a process of resolving the North Korean nuclear issue.
South Korea and the U.S. say it is necessary to guard against North Korea's missile and nuclear weapons activities that threaten South Korea, Japan, U.S. territories and possibly even the continental United States.
According to North Korean state media, as long as the U.S. continues its current policy, Kim Jong Un has ordered increases in the production of nuclear weapons and other offensive means, Abe said.
He added he explained to Abe the significance of the inauguration of the new administration and also its direction, and that the two spent some time dwelling on the North Korea nuclear issue, a common point of interest.
THAAD is expected to be a key topic for Hong's discussions with USA officials.
That suggests a range of 4,500 kilometers (2,800 miles) or more if flown for maximum distance, analysts said.More news: U.S. strikes Syria militia threatening U.S.-backed forces
South Korea's new liberal president vowed Thursday to reopen an investigation into the government's role in the violent suppression of a 1980 democratic uprising in the city of Gwangju that killed hundreds, as he further distanced himself from his ousted conservative predecessor. "(Seoul) must show that dialogue is possible only when North Korea changes its behavior".
"In order to diffuse the tension on the Korean Peninsula, the US must withdraw its forces from South Korea, stop its joint military games with South Korea and conclude a peace agreement with North Korea".
Hong Seok-hyun, a former ambassador to the United States, met with Trump for 15 minutes at the Oval Office with Vice President Mike Pence, National Security Advisor H.R. McMaster and senior White House advisor Jared Kushner by Trump's side, according to South Korean television network JTBC.
Haley said Sunday that cooperation with China has been better "than we ever have", and she expects it will produce dividends for the U.S.
The US Ambassador later tweeted: "There are no excuses that justify N. Korea's actions".
The Security Council first imposed sanctions on North Korea in 2006 and has stiffened them in response to its five nuclear tests and two long-range rocket launches.
Another carrier, the Ronald Reagan, left Yokosuka in Japan yesterday on its regular spring patrol, which would last three to four months, a spokesman for the U.S. Seventh Fleet said.