A spokesman for North Korea's Committee for the Peaceful Reunification of the Country said in the statement on Sunday that the goal of the training is to "totally destroy" North Korea, according to comments carried by North Korean state news agency KCNA.
"If there's an underground nuclear test, then you need to get ready for a very serious response by the United States", Senator Lindsey Graham said on CBS' "Face the Nation".
"I think it's increasing every day, which means that we are in a race, really, we are in a race to be able to solve this problem", McMaster told an audience at the Reagan National Defense Forum in Simi Valley.
But the American official told CNN that "the North Koreans had problems with re-entry", though an analysis of the test was continuing.
Still, the ability of the new missile to fly higher and longer than others in the past signals the program's intent to develop weapons capable of attacking the US.
Mr Graham said he has had extensive discussions with the Trump administration about the situation.
Still, he said, Pyongyang's actions had made America's alliances with Japan and South Korea "stronger than ever". "Not to contain it".
Cloaked with the world's most advanced stealth coating, the F-22s and F-35s would likely be called upon to lead a potential air campaign against North Korea should the situation escalate to the point of using military force, experts say.
Beijing has backed a slew of sanctions that include bans on imports of North Korean coal, iron ore and seafood.
But China has refused to turn off its pipeline shipping crude to North Korea. Pyongyang has been under United Nations sanctions since 2006 over its ballistic missiles and nuclear programs.
The North says the Hwasong-15 missile can be tipped with a "super-large heavy warhead" capable of striking the whole U.S. mainland.
Washington is battling to maintain global solidarity in the face of the North nuclear threat after Russian Federation warned that sanctions have failed and China sidestepped talk of an oil embargo.
But analysts remain unconvinced that the North has mastered the technology required to launch and direct a missile, and ensure it survives the hard re-entry into the Earth's atmosphere.