President Donald Trump, during a remarkable impromptu press conference, defended his mental fitness and declared himself willing to hold direct negotiations with North Korean leader Kim Jong Un. He also dug in on his demand that any immigration bill include funding for a U.S.-Mexico border wall.

Trump took questions at Camp David following a strategy session with GOP lawmakers, Cabinet officials and White House aides. He again denied he or his 2016 campaign colluded with Russia. While the president did not flatly deny dispatching aides to try stopping Attorney General Jeff Sessions from recusing himself from the Justice Department’s Russia probe, Trump contended he did nothing illicit.

Trump also sent a signal to congressional Democrats, saying he wants to legalize the Obama-era Deferred Action for Childhood Arrivals program — but only if a possible immigration bill also addresses his proposed southern border wall, something Democrats strongly oppose.

“We want the wall,” Trump said. “The wall’s going to happen or we’re not going to have DACA.”

Trump said he wants to address the DACA immigration program and funding for his southern border wall — and other related issues — in a single bill. But his demands again showed how difficult it will be to craft such a bill in an election year.

[Analysis: Five Ways Trump Dimmed the Tax Bill Glow]

“We want DACA to happen,” he said during an impromptu press conference at Camp David. “We have to get rid of the lottery system, we have to get rid of chain migration, we have to build the wall.”

Watch: Just How Realistic is Trump’s 2018 Legislative Agenda?

Mexico still will pay?

He also returned to promising that the Mexican government would pay for the border wall.

But after not mentioning that for months, he added a caveat:

“I believe that Mexico will pay for the wall. In some form, Mexico will pay for the wall,” Trump said.

He then mentioned the ongoing renegotiation of the North American Free Trade Agreement, a signal that changes to that pact might produce pro-U.S. effects that the president could claim are paying for the border barrier.

Remarkably, the president appears willing to talk to Kim, after some bluster about the United States’ nuclear arsenal. Trump said he is encouraged by North Korea-South Korea talks about the North possibly participating in the Winter Olympics in the South.

[Markey, Lieu Push ‘First Strike’ Bill After Trump Taunts Kim]

“Maybe they get involved in the Olympics, and things go from there,” he said. “I’d love to see them take it beyond the Olympics. … And at the appropriate time, we’ll get involved.”

Later, he was asked if he would have telephone conversations directly with Kim — and he responded he is open to that, just days after he let the young North Korean leader know in a Tweet that his “nuclear button” is “much bigger & more powerful” than the one on Kim’s desk.

“Sure, I always believe in talking,” he said. “Absolutely, I would do that.”

Pushing back

While Trump laid down a few policy markers, he also was asked about allegations by author Michael Wolff in a new book that his top aides view him as mentally unfit for the job. Specifically, Trump was asked why he felt a need to start Saturday with a series of morning tweets defending his mental state.

Now that Russian collusion, after one year of intense study, has proven to be a total hoax on the American public, the Democrats and their lapdogs, the Fake News Mainstream Media, are taking out the old Ronald Reagan playbook and screaming mental stability and intelligence…..

— Donald J. Trump (@realDonaldTrump) January 6, 2018

….Actually, throughout my life, my two greatest assets have been mental stability and being, like, really smart. Crooked Hillary Clinton also played these cards very hard and, as everyone knows, went down in flames. I went from VERY successful businessman, to top T.V. Star…..

— Donald J. Trump (@realDonaldTrump) January 6, 2018

….to President of the United States (on my first try). I think that would qualify as not smart, but genius….and a very stable genius at that!

— Donald J. Trump (@realDonaldTrump) January 6, 2018

“I went to the best colleges. I had a situation where I was an excellent student,” the president said. He went on to note his successes in the business and television realms before noting he captured the White House on his first-ever try.

“Then I hear this guy who … does not know me at all,” he said of Wolff, dismissing the author’s assessment of the president’s ability to do his job.

Wolff contends he spoke with Trump for nearly three hours — on the record — for his book, which Trump threatened a lawsuit to stop but did not act. The White House says they spoke only once, and briefly, but not for use in the book.

Trump continued his campaign to discredit Wolff by trying to connect him to former White House chief strategist and 2016 campaign adviser Steve Bannon, who is quoted in the book as questioning Trump’s mental state and smarts — while also slamming many of his immediate family members.

Trump responded this week by slamming Bannon, saying in an extraordinary statement on White House letterhead that his former aide “lost his mind” after being fired from his White House post.

On Saturday, Trump contended that Wolff must have gotten access to the White House via Bannon. He also suggested his former aide is on his way out at the conservative Breitbart news organization, saying “‘Sloppy Steve’ is looking for a job.” (Trump on Friday introduced that nickname for Bannon, adding it to the list of foes who’ve been labeled with an alternative and mocking moniker.)

The president also was asked to address a report that he asked top aides to lobby Sessions against recusing himself from the DOJ’s Russia probe.

“Everything I’ve done is 100 percent proper,” he said. “That is what I do: I do things proper.”

His critics, including most congressional Democrats, however, disagree.

He said a New York Times article on the demands of Sessions is “off,” but he declined to provide specifics.

He then reiterated his stance that “there’s been no collusion, there’s been no crime,” referring to the alleged campaign collusion. And he claims to still have confidence in Sessions, and said the probe is making America “look foolish” while declaring he wants it concluded soon.

After senior White House officials floated the idea of tackling Welfare and entitlement overhaul legislation as a top 2018 priority, Trump appeared to tamp down expectations. He said Republicans may put off a push for welfare overhaul legislation unless it is clear they have ample Democratic support.

[Democratic Candidate Misspeaks When Asked About Potential Influence]

Senate Majority Leader Mitch McConnell, R-Ky., who has been at Trump’s side during the Camp David meetings, has said that is a no-go since Democratic votes would be needed and no members of that party support the idea.

On the still-emerging GOP legislative agenda, McConnell indirectly addressed the shrunken Republican 51-49 majority that will require Democratic help to pass spending and policy legislation. McConnell said he thinks some Democrats will want to vote with Republicans on some agenda items.

House Speaker Paul D. Ryan, R-Wis., added to Trump’s list by calling legislation that addresses the income inequality gap, “the skills gap,” an infrastructure bill, and military funding top GOP priorities.

Notably, the three top GOP leaders did not mention any legislation to further erode or repeal the 2010 health law.

And in a lighter moment, Trump summoned chief economic adviser Gary Cohn to the podium when asked if the former Wall Street executive would be staying on.

Trump asked Cohn if he is happy in his current role amid reports Cohn, who is Jewish, was disgusted by his boss’s response to Nazi demonstrators at the deadly Charlottesville, Va., protests this summer.

“Yes, I’m happy,” Cohn said when pressed by the president.

But, in a classic Trumpian moment, the president, with his signature wry grin, told reporters this about a possible Cohn exit: “If he leaves, I’m going to say I’m happy he left.”