Trump says 2nd North Korea summit 'soon'

US President Donald Trump has said a second summit with North Korean leader Kim Jong-Un is likely to take place "quite soon".

Speaking at the United Nations, Trump said the relationship with the country whose leader he last year branded as "Little Rocket Man" is much improved.

"It was a different world. That was a dangerous time," Trump said on Monday.

"This is one year later, a much different time."

Trump said US Secretary of State Mike Pompeo is working out the details for the second Trump-Kim meeting.

Kim requested a second meeting with Trump in a letter this month, and Trump said, "we will be doing that".

The president is set to meet South Korea's Moon Jae-in to discuss North Korea and trade details.

Moon is expected to convey to Trump a personal message from Kim delivered at their inter-Korean talks last week.