"I would speak to him, I would have no problem speaking to him," the businessman said of Kim Jong-un.
The proposed meeting would mark a significant change of US policy towards the politically isolated regime.
Democrat front-runner Hillary Clinton responded by decrying his "bizarre fascination with foreign strongmen".
The statement, from one of her aides, added that Mr Trump's foreign policy "made no sense".
In a separate development, the BBC has learned that Mr Trump could visit the UK before the presidential election in November.
Diplomats expect his visit to the UK could happen after he formally becomes the Republican party candidate at a convention in July.
Mr Trump's comments about North Korea emerged in an interview with Reuters news agency on Tuesday, in which he also expressed disapproval of Russian President Vladimir Putin's military actions in eastern Ukraine.
Mr Putin is a figure who Mr Trump has previously said he respects.
On the subject of North Korea, the New York property developer said he would pursue face-to-face talks and added that he would also put pressure on China, as North Korea's only major ally.
North Korea first tested nuclear weapons in 2006, in breach of international agreements, and has made repeated threats of nuclear strikes against South Korea and the US.
Currently, any contact between with the US happens between officials, not at a presidential level.
North Korea does not have formal ties to many governments around the world
Whitehall diplomats may welcome Mr Trump before the November election
And he said he would dismantle most of the Dodd-Frank financial regulations if he is was elected president.
On Tuesday he released financial records claiming he holds $10 billion (£6.9 billion) in assets, although he has so far resisted calls from Democrats to release his full tax returns.
The visit to the UK is an intriguing prospect given the admission earlier this week from Mr Trump that "it looks like we're not going to have a very good relationship" with the UK.
British Prime Minister David Cameron has harshly criticised Mr Trump's proposed ban on Muslims coming to the US, calling his remarks "divisive, stupid and wrong".
Later on Tuesday the Mr Trump told Reuters that the prime minister's remarks are "totally inappropriate" but that "I'm sure I'll have a good relationship with him."
The new London mayor, Sadiq Khan, has also been in a verbal spat with Mr Trump, pushing back at the notion put forward by the American businessman that the Muslim mayor could be an "exception" to the ban.
Mr Trump owns property in the UK, including a golf course in Scotland, where his mother was born.