The US president has offered North Koreans a "path towards a much better future"
Donald Trump has said he will not "allow American cities to be threatened with destruction" as he again warned North Korea to underestimate US resolve.
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 between North Korea and its US-allied neighbours have been high due to the reclusive country's determination to pursue nuclear weapons.
Mr Trump told the National Assembly in Seoul: "The (North Korean) regime has interpreted America's past restraint as weakness.
"This would be a fatal miscalculation.
"This is a very different administration than the United States has had in the past."
In a stern warning to Pyongyang, Mr Trump said: "Do not underestimate us, do not try us.
"America does not seek conflict or confrontation, but we will never run from it. We will not permit America or our allies to be blackmailed or attacked."
He added: "The regime has pursued nuclear weapons with the deluded hope it could blackmail its way to the ultimate objective.
"And that objective we are not going to let it have.
"The North Korean regime has pursued its nuclear and ballistic missile programmes in defiance of every assurance, agreement and commitment it has made to the United States and its allies.
"It has broken all of those commitments."
Mr Trump offered North Koreans a "path towards a much better future", having urged the regime to "come to the table" and "make a deal" over its nuclear programme.
These were calls echoed by South Korean President Moon Jae-in when he joined Mr Trump for a news conference on Tuesday.
The US President was forced to cancel an unannounced visit to the de-militarised zone (DMZ) between North and South Korea due to bad weather.
The Marine One presidential helicopter left Seoul early on Wednesday and flew most of the way to the DMZ, but was forced to turn back just five minutes out due to fog.
Mr Trump heads to China later, where he is expected to seek President Xi Jinping's commitment to exerting further pressure on North Korea.
In his speech in Seoul, Mr Trump had singled out China, along with Russia, for its alliance with North Korea, saying: "You cannot support, you cannot supply, you cannot accept."
He also referenced the visit came a year on from his victory in the US election, adding he would be "celebrating" the achievement with the South Korean people.