McMaster was speaking hours after US and South Korean defense officials told CNN that an attempted missile launch by North Korea failed.
"Our commitment to this historic alliance to the courageous people of South Korea has never been stronger", Pence said remarks before troops at an Easter dinner.
McMaster, an Army lieutenant general, made the case for global action on the issue, including enlisting North Korean neighbour China, given the "brutality" of Kim's regime. Pence's visit, full of Cold War symbolism, comes amid increasing tensions and heated rhetoric on the Korean Peninsula. While the North did not conduct a nuclear test, the specter of a potential escalated USA response trailed Pence as he began a 10-day trip to Asia.
Liu Ming, from the Shanghai Academy of Social Sciences, said Beijing was unlikely to take further action at this stage unless Pyongyang carried out its sixth nuclear test or long-term ballistic missile test as Beijing insisted that talks, not military action, were the only solution to the North Korean issues.
"On this day I think of my dad", Pence said.
"We will respond to an all-out war with an all-out war and a nuclear war with our style of a nuclear attack", Choe said.
The US has leaned on China - North Korea's main ally - to apply pressure on Pyongyang to curtail its nuclear ambitions.
On Sunday, U.S. National Security Adviser H.R. McMaster said the problem with North Korea "is coming to a head".
"We've got a range of options, both militarily, diplomatic and others ... at disposal for the president should he choose to use them", the White House foreign policy adviser told reporters on Air Force Two.
A feared military confrontation between North Korea and the United States didn't materialize over the weekend, but tensions between the two countries remain dangerously high for the indefinite future.
After a two-month policy review, officials settled on a policy dubbed "maximum pressure and engagement", USA officials said Friday.
The Global Times newspaper, which does not necessarily reflect official policy, recommended that Beijing convey a clear message to Pyongyang: that if it conducts a sixth nuclear test, the Chinese government would support stiffer United Nations sanctions to cut off "the vast majority" of its oil supplies to North Korea.
The officials weren't authorized to speak publicly on the results of the policy review and requested anonymity.More news: United Airlines Scandal: CEO Says He's Embarrassed
Washington apparently coupled the show of force with a message for North Korean leader Kim Jong Un seeking to discourage him from escalating the tension, as US news media reported that the Trump administration decided not to seek a regime change in Pyongyang. "But dialogue for the sake of having dialogue is meaningless".
China, the North's sole major ally, and Russian Federation have both urged restraint, with Beijing's Foreign Minister Wang Yi warning that "conflict could break out at any moment".
North Korea's missile launch Sunday, despite its failure, underscored the country's defiance against the USA and gave no hint that Pyongyang will cease its acts of provocation.
Citing unnamed intelligence officials, NBC News reported Thursday that the USA was "prepared to launch a preemptive strike with conventional weapons" against North Korea in order to prevent an imminent nuclear test.
The launch, which ended with the missile exploding nearly immediately, came shortly before Vice President Mike Pence landed in South Korea for meetings with leaders there.
In contrast to his usual tone on Twitter, President Trump's response to the launch was muted. They have heard North Korean warnings of their destruction for so long that the threats barely even register. "So what we've seen here is an interaction between ourselves, our North Atlantic Treaty Organisation and other partners here, and especially our Afghan partners, and very determined and brutal enemies", he said. Trump tweeted on Sunday. According to Fox News, Deputy National Security Adviser K.T. McFarland declined to verify this account.
On Saturday North Korea displayed almost 60 missiles - including what is suspected to be a new intercontinental ballistic missile - at a parade to mark the 105th birthday of its founder Kim Il-Sung.
Into this tense environment, Pence made his first trip to the region since taking office in January.
Pence is joined by his wife and two adult daughters and will lay a wreath at the Seoul National Cemetery and join USA and South Korean troops for Easter Sunday church services and a dinner. Trump's answer: He is willing to unleash military power to eliminate any threat to the US homeland.
In a major symbolic move, Vice President Mike Pence on Monday will visit the Demilitarized Zone (DMZ), the highly fortified border between North Korea and South Korea.
At the same it's increased its military footprint in the region by deploying a naval carrier strike group to waters off the Korean Peninsula.
On Sunday morning, North Korea conducted a failed medium-range missile launch from a site near the northeastern coastal city of Sinpo.
"We know they have nuclear weapons, because they have conducted nuclear tests", he said.