Bolton quit the administration on Tuesday following disagreements with Trump on policies including how to denuclearize North Korea.

The hawkish adviser had once advocated for the "Libya model" that calls for North Korea to give up its nuclear weapons program before receiving any concessions in return.

"He made some very big mistakes. When he talked about the Libyan model for Kim Jong-un, that was not a good statement to make," Trump told reporters at the White House, referring to the North Korean leader. "You just take a look at what happened with Gaddafi. That was not a good statement to make, and it set us back."

Libya surrendered its weapons of mass destruction program in 2003, but its then-leader Muammar Gaddafi was toppled from power and killed by NATO-backed rebel forces in 2011.

North Korea has bristled at suggestions it should follow the same steps and vowed never to meet the same fate as the North African country.

"We were set back very badly when John Bolton talked about the Libyan model," Trump said. "And he made a mistake. And as soon as he mentioned that, the 'Libyan model,' what a disaster."

North Korea threatened to cancel the first summit between Kim and Trump in 2018 after Bolton spoke of the Libya model in relation to the North's denuclearization. Trump dismissed the notion at the time, and the summit went ahead as planned in Singapore in June.

"Take a look at what happened to Gaddafi, with the Libyan model. And he's using that to make a deal with North Korea?" Trump said of Bolton. "And I don't blame Kim Jong-un for what he said after that. And he wanted nothing to do with John Bolton. And that's not a question of being tough; that's a question of being not smart, to say something like that."

The timing of Bolton's departure coincided with North Korea's offer to resume denuclearization negotiations in late September.

The talks have been stalled since Trump and Kim's second summit in Vietnam in February ended without a deal due to differences over the scope of North Korea's denuclearization and sanctions relief from the US

Trump's comments on Wednesday could assure Pyongyang of Washington's commitment to providing the security guarantees it seeks in exchange for denuclearization.

"I really believe that North Korea would like to see something tremendous happen," Trump said, citing the country's economic potential.

"This could be one of the most unbelievable -- if you look at a country, in terms of upside, this could be one of the most unbelievable experiments ever: North Korea," he said.

Trump tweeted Tuesday that he had asked Bolton for his resignation. Bolton disputed the account, saying he had resigned of his own accord. (Yonhap)