Defying international pressure, the North test-fired another missile on Sunday as fears grow that it may also be preparing for its sixth nuclear weapons test.
"We hope to achieve this objective (the North's denuclearisation) through peaceful means but all options are on the table," Pence told a press conference in the South Korean capital after his trip to the tense border with the North.
"Just in the past two weeks, the world witnessed the strength and resolve of our new president in actions taken in Syria and Afghanistan.
"North Korea would do well not to test his resolve, or the strength of the armed forces of the United States in this region," Pence said at the press conference with South Korea's Acting President Hwang Kyo-Ahn.
Tensions between Pyongyang and Washington have soared in recent weeks, as a series of North Korean missile tests have prompted ever-more bellicose warnings from Trump's administration.
The new and inexperienced US president has indicated he will not allow North Korea to develop an intercontinental ballistic missile capable of delivering a nuclear warhead to the western United States.
Asked by a reporter what message he had for North Korean leader Kim Jong-Un in Washington on Monday, Trump replied "Gotta behave."
North Korea's envoy to the United Nations Kim In Ryong said the regime was preparing for "any mode of war" triggered by potential US military action, and said his country would respond to a missile or nuclear strike "in kind".
"If the United States dares opt for a military action... the DPRK is ready to react to any mode of war desired by the Americans," he told a news conference, using the country's official name, the Democratic People's Republic of Korea.
"We will take the toughest counteraction against the provocateurs."
Pence declared that the era of US "strategic patience" in dealing with the North was over, after more than two decades.
North Korea "answered our overtures with willful deception, broken promises and nuclear and missile tests", he said.
The United States, which stations 28,500 troops in South Korea, would "defeat any attack and we will meet any use of conventional or nuclear weapons with an overwhelming and effective response".
Still, White House press secretary Sean Spicer also sought to cool tensions during a news conference in Washington on Monday, saying Trump is not drawing "red lines" that would threaten military action against North Korea.
"Drawing red lines really hasn't worked in the past," he said. "He holds his cards close to the vest, and I think you're not going to see him telegraphing how he's going to respond to any military or other situation going forward."
Pence's visit came after a huge military parade Saturday during which North Korea showcased apparent intercontinental ballistic missiles, and as a US carrier group converges on the Korean peninsula.
It also came the day after North Korea's latest launch -- which failed when the missile blew up seconds after blast-off.
Speaking at the village of Panmunjom inside the DMZ, Pence said America's relationship with South Korea was "ironclad and immutable".
Pyongyang insists it needs a powerful arsenal -- including atomic weapons -- to protect itself from what it says is the ever-present threat of US invasion.
Pence urged the international community to join US and regional demands for an end to the North's nuclear and ballistic missile programmes.
"It is heartening to see China commit to these actions. But the United States is troubled by China's economic retaliation against South Korea for taking appropriate steps to defend itself," he said, referring to the US THAAD missile defence system.
The system being installed in South Korea is designed to shoot down missiles from North Korea or elsewhere. But China furiously objects to its deployment, saying it could spy on its own defence installations, and has taken apparent retaliatory action against South Korean firms operating in its country.
Pence said he and Trump "have great confidence that China will properly deal with North Korea".
"But as President Trump made clear just a few short days ago, if China is unable to deal with North Korea, the United States and our allies will."
This is Pence's first visit to South Korea -- part of an Asia swing that will also include stops in Japan, Indonesia and Australia -- and although it was conceived months ago, could hardly come at a time of higher tension.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)