"The future of this region and its attractive people must not be held hostage to a dictator's twisted fantasies of violent conquest and nuclear blackmail", he said during a speech in Vietnam at the annual Asia Pacific Economic Cooperation (APEC) forum.
A North Korean soldier was shot and injured by his own side Monday while defecting to South Korea at the truce village of Panmunjom, the South's military said.
Trump has been working to rally global pressure against North Korea's nuclear weapons program on a trip to Asia.
Pyongyang issued its retort Saturday branding Trump's Asia tour a "warmonger's visit for confrontation to rid the DPRK of its self-defensive nuclear deterrence", in the first comments on the visit by a North Korean official.
Nuclear-powered carriers USS Ronald Reagan, USS Nimitz and USS Theodore Roosevelt are taking part in the exercises, which will continue until Tuesday in the Sea of Japan, South Korea's Joint Chiefs of Staff (JCS) said.
The exercises will also involve 11 US Aegis ships and seven South Korean naval vessels, including two Aegis ships.
Trump has recently reiterated a sharp warning to North Korea during his speech in South Korea's parliament saying, "Do not underestimate us.
But our military is keeping a full readiness posture against the possibility of North Korea's provocations", a military official said in a briefing.
It's the first time since 2007 that three USA carrier strike groups have operated together in the Western Pacific.
In recent months, North Korea has tested intercontinental ballistic missiles and conducted it's most powerful nuclear test. Pyongyang also flew two missiles over Japan.
It has repeatedly threatened to launch ballistic missiles into the waters around the US territory of Guam.