The four-day exercise in the western Pacific involves USS Ronald Reagan, USS Nimitz and USS Theodore Roosevelt - as well as seven South Korean vessels, including three destroyers.
Though an armistice ceased fighting in that conflict, no peace treaty has ever been signed, and North Korea still tensely face off with South Korean and U.S. forces at the demilitarized zone that splits the Korean peninsula at the 38th parallel.
It is the first such U.S. triple-carrier drill in the region for a decade. Trump, being the man who he is, took the bait and threw some insults back at North Korean leader Kim Jong-un.
This isn't the first time Trump and Kim have traded barbs.
Kim's regime has continued to carry out nuclear and ballistic missile tests despite widespread worldwide condemnation and a series of crippling sanctions aimed at strangling the state's cash sources.
The US warships will carry out air defence drills, sea surveillance, defensive air combat training and other training operations, the US Navy said.
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With regard to the United States' handling of the threat posed by North Korea, Lee said President Trump's statements on the country and its leader Kim Jong Un have concerned some South Koreans but that Trump's actions show he is serious about addressing the issue.
Trump tweeted Saturday night. This isn't the first time North Korea have employed the 14th century term to insult Trump, with "dotard" sprinkled across a statement in September which ended: "I will surely and definitely tame the mentally deranged United States dotard with fire".
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.
Earlier, Chinese President Xi Jinping and President Trump reiterated firm commitment to achieving denuclearisation of the Korean Peninsula and working towards a solution through dialogue and negotiation.
Lee said Korea depends on a strong partnership with the U.S.in part because of its "very unique" geopolitical position close to world powers Japan and China and the communist regime of North Korea.
But experts doubt China will take the kind of steps that Trump wants, such as halting crude oil exports to the North.