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 it would not resume talks with the South until issues between the two are resolved.
Pyongyang has been angered by continuing US-South Korea joint military exercises which it sees as a rehearsal for invasion. It cancelled planned high-level talks with South Korea earlier this week.
In a statement, chief negotiator Ri Son-gwon reverted to the angry language the North has used before, describing South Korean authorities as incompetent and senseless in comments reported by state news agency KCNA.
He also criticised the South Korea for allowing "human scum" (a reference to a North Korean defector) to speak at the Seoul National Assembly.
Thursday's criticism of South Korea marks yet another shift in tone from Pyongyang just weeks before the planned US summit, the BBC's Laura Bicker in Seoul says.
Pyongyang appears to be putting pressure on both the US and South Korea and refusing to talk until some concessions are made, she adds.
What has Libya got to do with this?
North Korea's suggestion that it might pull out of the US summit pointed the finger squarely at US National Security Adviser John Bolton.
"We do not hide our feeling of repugnance towards him," said Wednesday's statement, which was written by Vice-Foreign Minister Kim Kye-gwan.
North Korea was apparently referencing an interview Mr Bolton gave comparing it to "the Libya model" of denuclearisation.
In 2003, Libya's Colonel Muammar Gaddafi agreed to give up his country's programmes of weapons of mass destruction in an announcement that surprised the world.
Most US sanctions on Libya were lifted within a few months and diplomatic ties between the countries restored. The North African country came in from the cold.
But in 2011 the authoritarian leader was toppled by rebels and militiamen backed by Nato. He was later captured and killed by rebel forces.
North Korea said last week it would begin dismantling its nuclear test site at Punggye-ri between 23-25 May, but there was no mention of allowing foreign experts access to the site.
On a recent visit to North Korea, US Secretary of State Mike Pompeo stressed that any claim of denuclearisation by the North would require a "robust verification" programme by the US and other nations.