Vietnam has eagerly courted trade and investment with the U.S. since Trump's election, more so after he yanked the United States from a key Pacific region trade pact, taking with him low tariff access to the world's largest market.
It referred to Trump as dotard, a word the reclusive nation has used on him in the past.
The United States has been sending its strategic assets, also including long-range bombers, to the region more frequently for patrols or drills amid accelerating North Korean efforts to expand its nuclear weapons program.
Asked about the possibility of becoming friends with the North Korean leader during a Sunday joint news conference in Vietnam, Trump did not rule it out.
During his trip to Asia, Trump attempted a symbolic stare-down of Kim this week at the heavily fortified border that separates North and South Korea. But heavy fog forced the cancellation of Trump's plans, and he was forced to turn back.
In the first comments on the U.S. leader's visit by a North Korean official, a Pyongyang foreign ministry spokesman said it was a "warmonger's visit for confrontation to rid the DPRK of its self-defensive nuclear deterrence", according to the state-run KCNA news agency.
In recent months, North Korea has tested intercontinental ballistic missiles that could reach the U.S. mainland with further development and has conducted its most powerful nuclear test.
"Dead stop. The flourishing ends, and the prison state of North Korea sadly begins".
This image shows three USA aircraft carriers.
The US warships will carry out air defence drills, sea surveillance, defensive air combat training and other training operations, the US Navy said. USS Theodore Roosevelt then will head to the Persian Gulf.
It's the first time since a 2007 exercise near Guam that three US carrier strike groups are operating together in the Western Pacific, according to the US Navy's 7th Fleet.
The army veteran said even limited military action against North Korea could cause a full-scale war leaving the USA "vastly outnumbered by North Korean forces".
The statement, which called the country's nuclear program "righteous and inevitable", continued: "He boasted about the "overwhelming superiority of USA power" and 'peace through strength.' But he needs to be well advised that it is the stand of the DPRK to defend our sovereignty and rights to existence and development by keeping a real balance of force with the U.S".