But at the same time, McMaster said on "This Week" on ABC that "it's time for us to undertake all actions we can, short of a military option, to try to resolve this peacefully".
To protect South Korea from North Korean missiles, the conservative government of former president Park Geun-hye agreed in July to deploy the Terminal High Altitude Area Defense (THAAD) system.
In the meantime, McMaster said President Trump is "determined" not to allow North Korea's nuclear capability to threaten the U.S.
Pence also addressed a series of concerns in Seoul since the onset of the US administration, including concerns in Seoul that Washington may unilaterally take military action or even order a pre-emptive strike on North Korea.
Chinese Foreign Ministry spokesman Lu Kang told reporters in Beijing the situation on the Korean peninsula was "highly sensitive, complicated and high risk", adding all sides should "avoid taking provocative actions that pour oil on the fire".
How did we get here?
Pyongyang did not conduct the anticipated nuclear test over the weekend but did hold a massive military parade on Saturday that exhibited some new long-range and submarine-based missiles, and attempted to test a medium-range missile on Sunday that exploded seconds after it was launched.
Its aim is to be able to put a nuclear warhead on an intercontinental ballistic missile that can reach targets around the world, including the US. "President Trump has made it clear that the patience of the United States and our allies in this region has run out", Pence said.
A US aircraft supercarrier is also en route to the Korean Peninsula, reports ABC's DAVID CAPLAN.
China has spoken out against North Korea's weapons tests and has supported United Nations sanctions.
OPINION: Will China intervene in North Korea? .
The Trump administration is making clear North Korea is a top foreign policy priority.
-TRUMP "WILL TAKE ACTION" TO END ANY NORTH KOREA THREAT TO US: TOP SECURITY ADVISER: Hours after North Korea paraded its weaponry and attempted a missile launch, President Trump's national security adviser said the USA leader will not allow Kim Jong Un's regime to have the capacity to threaten the USA, explains ABC's NICKI ROSSOLL.
The Walking Dead season 8: Steven Ogg, Pollyanna McIntosh, Katelyn Nacon promoted
Nacon is Enid, a teenage resident of Alexandria who has shown a connection to Carl. Ogg plays as Simon, Negan's right hand.
Keeping up the verbal volleying, North Korea's deputy U.N. ambassador accused the United States of turning the Korean peninsula into "the world's biggest hotspot" and creating "a risky situation in which a thermonuclear war may break out at any moment".
He reiterated United States support for South Korea, telling his host: "We are with you 100%".
During his visit to the Demilitarized Zone, Pence told CNN that the USA hopes to stop North Korea's nuclear program peacefully. Last week, Trump said he would not declare China a currency manipulator, pulling back from a campaign promise, as he looked for help from Beijing, which is the North's dominant trade partner.
North Korea has conducted five nuclear tests, including two previous year.
US President Donald Trump talked tough on the country's resolve, tweeting: "Our military is building and is rapidly becoming stronger than ever before".
"We need to apply pressure on North Korea so they seriously respond to a dialogue" with the global community, he said, urging China and Russian Federation to play more constructive roles on the issue.
The North casts the United States as the aggressor.
Downing Street would not be drawn on reports that Prime Minister Theresa May had privately urged Trump not to launch air strikes on North Korea.
"I think, in some way, my Dad just might be smiling from heaven to see the sacrifices that he and other American soldiers and South Korean soldiers made here are now passed on to my generation".
The North Korean regime began its nuclear program in earnest during the Clinton administration, which tried to prevent its buildup with a diplomatic agreement.
China has reiterated its call for North Korea to stop all tests, and has also called for a peaceful solution.
Chinese foreign ministry spokesman Lu Kang said in a daily briefing Monday that the onus was on all parties - including the USA and China - to reach a peaceful solution.
The vice president says the USA wants to achieve this through peaceful means, but all options are on the table.
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