But the vice president expressed impatience with the unwillingness of North Korea to move toward ridding itself of nuclear weapons and ballistic missiles.
Earlier, after discovering "great chemistry" with Chinese President Xi Jinping over "the most attractive piece of chocolate cake" at Mar-a-Lago, Trump had confided, "I explained. that a trade deal with the USA will be far better for them if they solve the North Korean problem!"
She added, "The main reason why we are proceeding with this is that there is this imminent threat from North Korea that threatens South Korea, threatens our allies, and threatens our troops in the region".
The US, Japan, South Korea and China have attempted to reign in the reclusive nation for decades.
China, North Korea's only ally who President Trump is relying on to influence Pyongyang, has repeatedly called for calm amid increasing sabre-rattling on both sides.
Pence had struck a more conciliatory tone at a press conference with the Japanese Deputy Prime Minister Taro Aso in Tokyo Tuesday.
Mr Abe said it was a "matter of paramount importance for us to seek diplomatic efforts as well peaceable settlements of the issue".
"If the United States is unwilling to negotiate with North Korea, and the regime is unwilling to abandon its nuclear and missile programs based on pressure alone, the prospect of the United States using military action to prevent North Korea from developing the capability to strike the continental United States becomes more likely".
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The event has been traditionally arranged by USA first ladies since 1878. "Think of it - 139", he said. The president also thanked Barron for attending the event before inviting the first lady to speak.
North Korea will continue to test missiles regularly and any military action against it by the United States would prompt "all-out war", a senior North Korean official tells the BBC.
According to the statement, Seoul, Washington and Tokyo also used the DTT as an opportunity to assess the results of recent joint military drills conducted by the three allies in South Korean and Japanese waters, including a trilateral anti-submarine warfare exercise conducted for the first time this year in April. As 80 percent of Pyongyang's trade comes through China, Trump believes that Beijing can force Kim to stop testing missiles and atomic bombs before he produces an intercontinental ballistic missile that could hit the U.S.
He did not comment on what might have caused the missile to fail but a n official said the missile was a Scud variant that the United States calls a KN-17.
The country's Vice-Foreign Minister, Han Song-ryol, told the BBC Monday that North Korea would continue to test missiles "on a weekly, monthly and yearly basis", and warned an "all-out war" would result if the US took military action.
"It's important that North Korea know we are not trying to pick a fight, so don't try to give us one", Haley told reporters.
And while the tensions with North Korea have dominated Pence's trip, the goal of it is to promote USA trade in the region.
While many details about North Korea's nuclear missile technology are likely not publically available, Mann may have likely been referring to the often-cited North Korea's Taepodong 2 long-range missile.