In the first comments on Mr Trump's visit by a North Korean official, a Pyongyang foreign ministry spokesman said it was a "warmonger's visit for confrontation to rid" North Korea of its self-defensive nuclear deterrence, the state-run KCNA news agency reported.
The paper denounced the US president's Asia trip as "a warmonger's trip for confrontation with the North", "an old miser's trip to sell arms", and "a chief terrorist's trip for self-destruction".
Trump had also delivered a sharp warning to North Korea in a speech at South Korea's parliament on Wednesday, telling the country: "Do not underestimate us".
Also on Saturday, the US and South Korean navies launched four days of joint drills off the east coast of South Korea.
The three carriers will be likely together in the drills around Monday, according to a South Korean military official, who didn't want to be named, citing office rules.
Three U.S. aircraft carriers joined an ongoing exercise with the South Korean Navy in the East Sea on Sunday in an unprecedented show of force against a provocative North Korea.
Trump is in Vietnam as part of a five-nation tour of Asia and North Korea's nuclear weapons programme has been a major talking point with his Japanese, South Korean and Chinese counterparts.
A total of seven South Korean navy vessels, including Aegis-equipped warships, will participate in the drill, the statement said, to accompany 14 US naval warships.
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.
The harsh words between the leaders have escalated in recent months after North Korea threatened to launch missiles toward the United States territory of Guam.
It has repeatedly threatened to launch ballistic missiles into the waters around the US territory of Guam.