In 2003, Libya’s leader Muammar Gaddafi agreed to give up his nuclear programme but was killed by western-backed rebels years later.
The suggestion, put forward by his national security adviser John Bolton, prompted alarm in North Korea.
Mr Trump said he still thought a summit with the North would happen.
North Korea warned on Wednesday that it might not attend the talks, due to take place in Singapore on 12 June.
What did President Trump say?
As Mr Bolton looked on, the US president said: “The Libyan model isn’t a model that we have at all when we’re thinking of North Korea.
The deal Mr Trump was considering with Kim Jong-un would be “something where he’d be there, he’d be in his country, he’d be running his country, his country would be very rich.
“If you look at South Korea, this would be really a South Korean model in terms of their industry… they’re hard-working, incredible people.”
On the planned summit, Mr Trump said: “Nothing has changed on North Korea that we know of. We have not been told anything.
“And if it does that’s fine and if it doesn’t I think we’ll probably have a very successful meeting.”
How does North Korea see it?
Also on Thursday, North Korea said…