"We'll be conducting more missile tests on a weekly, monthly and yearly basis", Vice Foreign Minister Han Song-Ryol told the BBC's John Sudworth in Pyongyang.
"We will take the toughest counteraction against the provocateurs", said Kim.
Vice President Pence visited the Korean Demilitarized Zone on Monday, not only warning North Korea that the US "era of strategic patience" with Pyongyang is over, but unexpectedly going all the way forward to the military demarcation line, a part of the heavily guarded border between North Korea and South Korea.
North Korea revealed a special fighting force during a weekend military parade.
The US Pacific Command statement said: "The Command detected and tracked what we assess was a North Korean missile launch. President Trump has made it clear that the patience of the United States and our allies in this region has run out", Pence said.
Noting 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.
North Korean Leader Kim Jong Un observes a target-striking contest by the Korean People's Army (KPA).
He warned that as long as the United States and its allies "scheme to bring down the socialist system in the DPRK", the government will keep increasing "its military muscle" to protect the country.
North Korea has taken "self-defensive" measures in response to U.S. threats of military action and these reflect Pyongyang's determination to "counter nukes and ICBM in kind", he said, referring to intercontinental ballistic missiles.
"The KPA will deal deadly blows without prior warning any time as long as the operation means and troops of the US and South Korean puppet forces involved in the "special operation" and "preemptive attack" targeting the [Democratic Republic of Korea] remain deployed in and around South Korea", the North Korean military warned in late March.
The vice president says the USA wants to achieve this through peaceful means, but all options are on the table.
Chinese Foreign Minister Wang Yi said: "If a war occurs, the result is a situation in which everybody loses and there can be no victor".
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.
North Korea has accelerated its nuclear and missile tests in recent years, despite global condemnation and United Nations sanctions.
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.
The U.S. moves an huge warship to the waters off the peninsula in a display of military might.
The Chinese Foreign Ministry's spokesman, Lu Kang, tried to calm the waters in a press conference Monday.
How advanced is North Korea's nuclear programme?
In Moscow, Russian Foreign Minister Sergey Lavrov, speaking to reporters Monday evening, said he hoped there would 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".
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Tuesday's meeting will mark the first time that senior advisers to the president have a formal discussion about Paris. The head of the Environmental Protection Agency has called for America to "exit" the Paris Climate Agreement.