The four-day drills that began in waters off South Korea's eastern coast come as President Donald Trump continues a visit to Asia that has been dominated by discussions over the North Korean nuclear threat.
Trump is now in Vietnam attending the Asia-Pacific Economic Cooperation summit, but he took the time to tweet: "Why would Kim Jong-un insult me by calling me 'old, ' when I would NEVER call him 'short and fat?'".
In a speech to South Korea's Parliament on Wednesday, Mr Trump warned Pyongyang not to underestimate the USA, while offering leader Kim Jong Un a better future if he gives up his nuclear ambitions.
Trump is in Vietnam as part of a almost two-week tour of Asia, and North Korea's nuclear weapons program has been a major talking point with his Japanese, South Korean and Chinese counterparts. That includes a stern speech delivered in South Korea's National Assembly on Tuesday, in which he said: "Do not underestimate us. And do not try us".
Following his stop in South Korea, the President travelled on to China - North Korea's biggest ally and trading partner. He said "every single step the North Korea regime takes toward more weapons is a step it takes into greater and greater danger".
On Saturday, Kim's government responded by accusing Trump of trying to demonize North Korea, keep it apart from the global community and undermine its government.
Trump told an audience of CEOs at the Asia-Pacific Economic Cooperation summit in Danang, Vietnam, that the region's future "must not be held hostage to a dictator's twisted fantasies of violent conquest and nuclear blackmail".
Speaking later in Vietnam's capital, Hanoi, Trump said "it would be very, very nice" if he and Kim became friends.
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.
Trump followed up his weird tweet by telling reporters that it would be a "good thing" for him and dictator to become friends.
Mr Trump also urged other nations to join forces to combat the growing threat posed by Pyongyang.
For the last months, the two leaders have been on two ends of a bitter war of words prompted in part by Pyongyang refusal to cease ballistic missile tests and the development of nuclear capabilities.
- DeShone Kizer leaves Browns vs. Lions game with injury
- 'Rare opportunity': Pentagon confirms joint drill of 3 aircraft carriers in Pacific
- Celebrities React to Taylor Swift's 'Reputation' - See Their Posts!
- Patriots bring back former tight end, Martellus Bennett
- NRSC ends fundraising agreement with Roy Moore
- Injured in France After Driver Rams Into Group of Students
- Odd-even scheme to be back? NGT to decide today
- Kevin Spacey dropped from film after fresh sexual allegations
- Conor McGregor Shoves Ref, Slaps Security Guard At Bellator Event
- Ivory Coast wanted Bakayoko to represent them over France