North Korea is also stepping up diplomatic actions to seek support and understanding from other countries over its missile launch.
The latest missile flew about 500km, the Joint Chiefs of Staff said, according to South Korean news agency Yonhap.
However, North Korea does not seem willing to stop its missile launches, including nuclear ones.
China for its part has been infuriated by the US deployment of an advanced Terminal High Altitude Area Defense (THAAD) anti-missile system in South Korea, saying it was a threat to its security and would do nothing to ease tension with Pyongyang.
North Korea said it had developed a nuclear warhead small enough to be fitted atop a missile.
China urged the United States and North Korea to commit to a political decision to solve the "nuclear problem".
Moon's office announced on Tuesday that he accepted an offer by President Donald Trump to visit the White House; the two will meet in Washington in June to discuss a new approach that might bring North Korea to the bargaining table.
The launch came a week after North Korea successfully tested a new midrange missile that it said could carry a heavy nuclear warhead.
"Well, I think you first have to get into Kim Jong-un's head, you know, which is he's in a state of paranoia", Haley, the United States' ambassador to the United Nations, said on "This Week," about the North Korean leader.
It "represents a level of performance never before seen from a North Korean missile", aerospace engineering specialist John Schilling wrote on the respected 38 North website.
The North defends its weapons programs as necessary to counter US hostility and regularly threatens to destroy the United States.
"They have the overwhelming dominant economic relationship with North Korea and because they have the greatest leverage, they have the great responsibility", the Australian leader said.
People cheer as missile developers arrive in Pyongyang, North Korea.
Kim accused the council of playing "to the tune of the USA again" and protested the Trump administration's demand for countries to choose allegiance between the United States and the Democratic People's Republic of Korea, his country's official name.
The disputed NLL lies in the Yellow Sea the between South and North Korea and is considered the de facto maritime boundary between them.
Trump warned in an interview with Reuters this month that a "major, major conflict" with North Korea was possible, and in a show of force, sent the Carl Vinson aircraft carrier strike group to Korean waters to conduct drills with South Korea and Japan.
This data underlines the progress made by Pyongyang in its efforts to develop an intercontinental nuclear missile in the future that can reach the United States.