Earlier, Pence called North Korea's failed missile launch a "provocation".
The 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.
U.S. Vice President Mike Pence says the "era of strategic patience is over" with North Korea, expressing impatience with the unwillingness of the North Korean regime to move toward ridding itself of nuclear weapons and ballistic missiles.
He says there was a "period of patience" over the years but "the era of strategic patience is over".
"North Korea is a liability to everybody and it's a threat not just to the United States, not just to South Korea, not just to Japan, not just to Russian Federation, but it's actually a threat to China as well", McFarland said Sunday on "Fox News Sunday".
McMaster said Trump has made clear he will not allow the nuclear-armed Pyongyang regime to put the United States and its regional allies under threat.
In Moscow, Russian Foreign Minister Sergey Lavrov, speaking to reporters Monday evening, said he hopes the United States "there will be no unilateral actions like those we saw recently in Syria and that the USA will follow the line that President Trump repeatedly voiced during the election campaign".
During a fellowship meal after the services, he said the tensions on the Korean peninsula had put into sharp focus the importance of the joint U.S. The U.S. military has about 28,500 troops stationed in South Korea.
The White House foreign policy adviser traveling with Pence told reporters that the type of missile that North Korea tried to fire on Sunday was medium-range, and that it exploded about 4 to 5 seconds after it was launched.More news: Padres activate Cahill from DL to start against Braves
Without going into specifics to avoid telegraphing American plans, McMaster said that the administration will do what is necessary to prevent North Korea from putting American lives in danger.
Earlier, as Pence visited the nearby Camp Bonifas, a US-led United Nations command post, he said: "It is particularly humbling for me to be here, ".
"My father served in the Korean war with the U.S. Army, and on the way here we actually saw some of the terrain [where] my father fought alongside Korean forces to help earn your freedom".
Pointing to Trump's recent military actions in Syria and Afghanistan, Pence said, "North Korea would do well not to test his resolve", or the US armed forces in the region.
During an Easter ceremony and dinner with American troops and their families in Seoul on Sunday night, Pence did not mention the latest North Korean threats but thanked the troops for their efforts at a tense time in the region. Foreign Ministry spokesman Lu Kang said Monday that tensions need to be eased on the Korean Peninsula to bring the escalating dispute there to a peaceful resolution.
Trump wrote Sunday on Twitter that China was working with the United States on "the North Korea problem".
While the North did not conduct a nuclear test, the specter of a potential escalated US response is trailing Pence as he undertakes a 10-day trip to Asia amid increasing tensions and heated rhetoric.
Before a smiling Kim Jong-un, North Korea presented several new weapons Saturday at a military parade celebrating the 105th anniversary of the birth of DPRK founder Kim Il Sung.
The national security adviser said that the administration's recent actions in Syria and elsewhere have demonstrated that Trump "is comfortable making the tough decisions". "And so it's time for us to undertake all actions we can, short of a military option, to try to resolve this peacefully".
Recent reports suggest that the USA will adopt a more forceful approach if North Korea decides to follow through with its plans; however, it is unclear what specific actions the administration will take.