President Trump is considering five candidates to replace John Bolton as national security adviser, and will announce his pick sometime next week, he announced Wednesday. He spoke to reporters during an unrelated event on his desire to ban flavored e-cigarettes.

"I have five people that want it very much," Mr. Trump said about the contenders to replace Bolton, calling the candidates "good people I've gotten to know" during his tenure. The president added that he would "be announcing somebody next week."

Mr. Trump announced that Bolton was leaving the administration on Twitter on Tuesday.

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"I informed John Bolton last night that his services are no longer needed at the White House. I disagreed strongly with many of his suggestions, as did others in the Administration, and therefore...I asked John for his resignation, which was given to me this morning. I thank John very much for his service. I will be naming a new National Security Advisor next week," Mr. Trump wrote.

Mr. Trump reiterated that he had disagreed with Bolton on several issues, including Bolton's desire to take the "Libyan model" to North Korea.

In 2018, Bolton said on "Face the Nation" that he was "looking at the Libya model of 2003, 2004" as a model for a nuclear deal with North Korea.

In 2003, Libya negotiated sanctions relief from the United States in exchange for renouncing its nascent nuclear program. Eight years later, Libyan leader Muammar Gaddafi was overthrown in a gruesome killing by Western-backed rebels.

"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. You just take a look at what happened with Gaddafi. That was not a good statement to make. And it set us back," Mr. Trump said of Bolton.

Mr. Trump also told reporters that he disagreed with Bolton's stance on Venezuela. In August, Bolton told reporters that the U.S. was readying measures to respond to Venezuelan President Nicolás Maduro "that will show the determination that the United States has to get a peaceful transfer of power."

"I wish John the best, we actually got along very well," Mr. Trump said, although he acknowledged Bolton might want to "spin it his way."

Bolton has disputed Mr. Trump's claim that he asked for Bolton's resignation, saying that he offered to resign.

"I offered to resign last night and President Trump said, 'Let's talk about it tomorrow,'" Bolton wrote on Twitter, slightly contradicting Mr. Trump's account that he had asked for Bolton's resignation.

"Hopefully we parted in good stead, but maybe we haven't, we will see," Mr. Trump said Wednesday.

Kathryn Watson contributed to this report.