On Friday he warned world leaders gathered in the Vietnamese resort city of Danang that the Asia-Pacific region "must not be held hostage to a dictator's twisted fantasies".
The US President was speaking during an official visit to the South Korean capital as he seeks to build unity in the region on the issue of North Korea.
Tensions over North Korea's weapons programme have surged in recent months, as Pyongyang carried out a sixth nuclear test - by far its largest to date - and test fired dozens of missiles, some capable of reaching the U.S. mainland.
At a speech in South Korea's parliament on Wednesday, Trump denounced the North's "cruel dictatorship" but appeared to moderate his bellicose tone somewhat when he offered Pyongyang a "path to a better future".
The North on Saturday said Trump's warnings "can never frighten us or put a stop to our advance", according to the state-run KCNA news agency, quoting a Pyongyang foreign ministry spokesman. "On the contrary, all this makes us more sure that our choice to promote economic construction at the same time as building up our nuclear force is all the more righteous, and it pushes us to speed up the effort to complete our nuclear force".
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He leaves for the Philippines on Sunday afternoon where he will attend the ASEAN summit of Southeast Asian leaders.
The army veteran said even limited military action against North Korea could cause a full-scale war leaving the U.S. "vastly outnumbered by North Korean forces". "We will not be intimidated", he told South Korean lawmakers.
The exercises will also involve 11 US Aegis ships and seven South Korean naval vessels, including two Aegis ships.
Tensions between North Korea and its US-allied neighbours have been high due to the reclusive country's determination to pursue nuclear weapons.
Joseph Yun, the State Department's top North Korea official, told the Council on Foreign Relations on October 30 that the USA would resume direct dialogue with Pyongyang if it ceased missile tests for 60 days, sources told The Washington Post.
The expert said they do not have a specific policy of pre-emptive strikes prior to launch and if the U.S. were to launch a missile, North Korea could claim they have been attacked.