The drills began in waters off South Korea's eastern coast.
The South Morning China Post quoted military officials describing this as a clear warning to North Korea, which involve three US aircraft carriers.
South Korean warships joined three US aircraft carriers Saturday in an unusually strong display of naval force aimed at North Korea, whose nuclear ambitions have been a focus of US President Donald Trump's ongoing tour of Asia.
According to the U.S. Navy, it is the first three-carrier exercise in the Western Pacific since 2007.
Trump has traded insults and threats with Kim in the past amid escalating tensions over Pyongyang's nuclear and missile programs.More news: US, South Korea joint military drills begin in Western Pacific
North Korea is not known to have tested any of its missiles or nuclear devices since September 15, a relative lull after a brisk series of tests earlier this year.
One of Trump's tweets read: "Why would Kim Jong-un insult me by calling me 'old, ' when I would NEVER call him 'short and fat?' Oh well, I try so hard to be his friend - and maybe someday that will happen!" The post came in response to the country's foreign ministry calling Trump "an old lunatic" over his speech in South Korea.
November 11: United States and South Korea on Saturday started joint naval four-day drills to warn the North Korea.
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.
Currently, he is in Vietnam where he took part in Asia-Pacific Economic Cooperation (APEC) Summit.More news: Moore Sexual Harassment Claims; GOP Congress ignore Obamacare defunding
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".
Though China has backed United Nations sanctions, USA officials want Chinese authorities to clamp down on unauthorised trade along the North Korean border.
Trump has been working to rally global pressure against North Korea's nuclear weapons program on the trip to Asia.
But experts doubt China will take the kind of steps that Trump wants, such as halting crude oil exports to the North.More news: First look at Doctor Who's brand new costume