Mike Pence - who is visiting South Korea and Japan - has warned that "the era of strategic patience is over"
Donald Trump has warned North Korea it has "gotta behave" as the US agreed to the early deployment of a missile defence system in the region.
Asked about his next move after Pyongyang's failed missile launch on Sunday, the President said: "You'll see".
Expanding on Mr Trump's remarks, White House press secretary Sean Spicer said the President would not be "drawing lines in the sand" over rising tensions in the Korean peninsula.
He said: "(Mr Trump) holds his cards close to the vest. I think you're not going to see him telegraphing how he's going to respond to any military or other situation going forward."
The President's warning comes as North Korea's deputy UN ambassador accused the US of creating "a dangerous situation in which a nuclear war may break out at any moment."
Earlier, Vice President Mike Pence warned it would be unwise to test the "resolve" of Mr Trump and said "all options are on the table" to deal with the threat posed by Pyongyang.
During a visit to South Korea, he travelled to the Demilitarised Zone dividing the two states, which technically remain at war after the 1950-53 Korean war ended in a truce and not a peace treaty.
The unannounced trip allowed the Vice President, whose father fought in the Korean War, to look at North Korean soldiers from afar and gaze directly across a border marked by razor wire.
As Mr Pence was briefed near the military demarcation line, two North Korean soldiers watched on, with one taking photographs of the vice president.
He told reporters that President Trump was hopeful China would use its "extraordinary levers" to pressure Pyongyang to abandon its weapons programme.
Mr Pence - who has since arrived in Japan as part of his visit to south-east Asia and Australia - voiced impatience with the unwillingness of Kim Jong-Un's regime to move towards getting rid of its nuclear weapons and ballistic missiles.
Pointing to the quarter-century since the US first confronted the North over its attempts to build nuclear weapons, the Vice President said this had been followed by a period of patience.
"But the era of strategic patience is over," he declared.
"President Trump has made it clear that the patience of the United States and our allies in this region has run out and we want to see change.
"We want to see North Korea abandon its reckless path of the development of nuclear weapons, and also its continual use and testing of ballistic missiles is unacceptable."
On Sunday, Mr Trump wrote on Twitter that China was working with the US on "the North Korea problem".
US officials said the Trump administration has settled on a policy dubbed "maximum pressure and engagement" after a two-month policy review.
Mr Pence sought to explain this policy in meetings with South Korea's acting president and other top officials in Seoul at the start of the trip, which will also include stops in Indonesia and Australia.