The drills began in waters off South Korea's eastern coast.
It comes on the same day Rodong Sinmun, the regime-run newspaper, warned the North would "surely win in the showdown" with the US and South Korea.
Trump is overseas on a 12-day Asia-Pacific trip during which he has been meeting with regional leaders with a heavy emphasis on curbing North Korea's nuclear and missile programs.
According to the U.S. Navy, it is the first three-carrier exercise in the Western Pacific since 2007.
The threat of conflict between Kim Jong-un's nuclear-armed North and the South, backed by Donald Trump, has been looming over the Korean Peninsula for months.
Kim's regime has continued to carry out nuclear and ballistic missile tests despite widespread global condemnation and a series of crippling sanctions aimed at strangling the state's cash sources. Trump fired back hours later in a sarcastic tweet going after the dictator's weight and height.
"I think from the USA point of view, Korea will continue to be a key part for peace and stability, and we have similar interests in east Asia", he said.More news: Pentagon: Ground Invasion the Only Way to Destroy North Korea Nukes
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South Korea and the United States will conduct a massive joint naval exercise involving three USA aircraft carriers off the eastern coast Saturday in an unprecedented show of force aimed at deterring North Korea.
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.
Trump sent out the tweet after he attended the Asia-Pacific Economic Cooperation (APEC) summit in Vietnam.
During talks in Beijing Thursday, Trump urged Chinese leader Xi Jinping to work hard and act fast to help resolve the North Korean nuclear crisis, warning that "time is quickly running 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.
He called on nations to stop financing and trading with North Korea.
But experts doubt China will take the kind of steps that Trump wants, such as halting crude oil exports to the North.