"But all options are on the table as we continue to stand shoulder to shoulder with the people of South Korea for denuclearization of this peninsula and for the long-term prosperity and freedom of the people of South Korea", Pence said.
Mr Han told the BBC: "If the U.S. is planning a military attack against us, we will react with a nuclear pre-emptive strike by our own style and method".
"Over the past 18 months, North Korea has conducted two unlawful nuclear tests and an unprecedented number of ballistic missile tests, even conducting a failed missile launch as I traveled here for this visit".
Pyongyang insists it needs a powerful arsenal - including atomic weapons - to protect itself from what it says is the ever-present threat of invasion by hostile United States forces.
Lotte, the South Korean conglomerate which turned over land to use for THAAD, has faced huge losses as 87 of its 99 stores have reportedly been closed in China, mostly for ostensibly breaching fire regulations.
Commuters ride on an electric trolley Monday in Pyongyang, North Korea.
Russian Federation on Monday warned Washington against launching a unilateral strike on North Korea, after US Vice President Mike Pence said the era of "strategic patience" with Pyongyang was over.
"Just in the past two weeks, the world witnessed the strength and resolve of our new president in actions taken in Syria and Afghanistan", Mr Pence said.
Pence's visit to the tense DMZ dividing North and South Korea came at the start of a 10-day trip to Asia and underscored US commitment.
North Korea's special operations forces could be used to counter allied pre-emptive strike plans.
What the Kim Jong-un regime did not do, however, was test another nuclear device, something that many had feared would lead to retaliation from the Trump administration, where rhetoric against the North Korean government has become increasingly harsh.More news: Talk-radio host Alex Jones argues persona in custody dispute
More news: Protesters gather on Tax Day to demand Trump release tax returns
More news: Kendrick Lamar's new album samples conservative news broadcaster
But Trump has also shown he is willing to link trade to other issues, saying he would cut a better trade deal with China if it exerts influence on North Korea to curb its nuclear ambitions.
Commuters ride on an electric trolley in Pyongyang, North Korea.
"The people of North Korea, the military of North Korea should not mistake the resolve of the United States of America to stand with our allies".
"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", Kim said.
The North regularly launches short-range missiles, but is also developing mid- range and long-range missiles meant to target US troops in Asia and, eventually, the USA mainland.
The unannounced visit Monday at the start of his 10-day trip to Asia was a USA show of force that allowed the vice president to gaze at North Korean soldiers from afar and stare directly across a border marked by razor wire.
He said the USA was "disturbing global peace and stability and insisting on the gangster-like logic that its invasion of a sovereign state is decisive and just and proportionate and contributes to defending the worldwide order".
Trump acknowledged on Sunday that the softer line he had taken on China's management of its currency was linked to its help on North Korea.
Speaking Sunday, US national security adviser H. R. McMaster said that when it came to the North Korean nuclear program "all of our options are on the table, undergoing refinement and further development".
In Moscow, Russian Foreign Minister Sergey Lavrov, speaking to reporters Monday evening, said he hopes "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".
Japanese Prime Minister Shinzo Abe on Monday told a parliamentary session that diplomatic efforts were "important to maintain peace", but "dialogue for the sake of having dialogue is meaningless".