WASHINGTON — President Trump, whose sometimes erratic behavior in office has generated an unprecedented debate about his mental health, declared on Saturday that he was perfectly sane and accused his critics of raising questions to score political points.

In a series of Twitter posts that were extraordinary even by the standards of his norm-shattering presidency, Trump insisted that his opponents and the news media were attacking his capacity because they had failed to prove that his campaign conspired with Russia during the 2016 presidential campaign.

“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,’’ he wrote on Twitter, even as a special counsel continues to investigate the Russia matter.

“Actually, throughout my life, my two greatest assets have been mental stability and being, like, really smart,’’ he added. He said he was a “very successful businessman’’ and television star who won the presidency on his first try. “I think that would qualify as not smart, but genius . . . and a very stable genius at that!’’

Elaborating during a meeting with reporters at Camp David later in the day, Trump again ticked off what he called a high-achieving academic and career record. He raised the matter “only because I went to the best colleges, or college,’’ he said.

Referring to a new book citing concerns about his fitness, he said, “I consider it a work of fiction and I consider it a disgrace.’’

The president’s engagement on the issue is likely to fuel the long-simmering argument about the president’s state of mind that has roiled the political and psychiatric worlds and thrust the country into uncharted territory.

Some Democrats in Congress have introduced legislation to force the president to submit to psychological evaluation. Mental health professionals have signed a petition calling for his removal from office. Others call armchair diagnoses a dangerous precedent or even a cover for partisan attacks.

In the past week alone, a new book resurfaced previously reported concerns among the president’s own advisers about his fitness for office. The author said the question of his mental state came up at two White House briefings and the secretary of state was asked if Trump was mentally fit.

After the president boasted that his “nuclear button’’ was bigger than Kim Jong Un’s in North Korea, Richard W. Painter, a former adviser to President George W. Bush, described the comment as proof that Trump is “psychologically unfit’’ and should have his powers transferred to Vice President Mike Pence under the Constitution’s 25th Amendment.

Trump’s self-absorption, impulsiveness, lack of empathy, obsessive focus on slights, tenuous grasp of facts, and penchant for sometimes far-fetched conspiracy theories have generated endless op-ed columns, magazine articles, books, professional panel discussions, and cable television speculation.

“The level of concern by the public is now enormous,’’ said Bandy X. Lee, a forensic psychiatrist at Yale School of Medicine and editor of “The Dangerous Case of Donald Trump: 27 Psychiatrists and Mental Health Experts Assess a President,’’ a book released last fall.

“They’re telling us to speak more loudly and clearly and not to stop until something is done, because they are terrified,’’ Lee said.

As Politico reported, Lee was invited to Capitol Hill last month to meet with about a dozen members of Congress to discuss the matter. But all but one of the lawmakers she briefed are Democrats.

While some Republicans have raised concerns, they do so mostly in private. Others scoff at the question, dismissing it as outrageous character assassination.

Few questions irritate White House aides more than inquiries about the president’s mental well-being, and they argue that Trump’s opponents are trying to use those questions to achieve what they could not at the ballot box.

“This shouldn’t be dignified with a response,’’ said Kellyanne Conway, the White House counselor.

“The partisans on Capitol Hill consulting with psychologists should reorient their spare time: Support the president’s positive agenda of middle class tax cuts, rebuilding infrastructure and the military, investing in our workforce,’’ Conway said later in an e-mail. “The never-ending attempt to nullify an election is tiresome; if they were truly ‘worried about the country,’ they’d get to work to help it.’’

Thomas J. Barrack, a friend of Trump’s, was quoted in Michael Wolff’s new book, “Fire and Fury: Inside the Trump White House,’’ as telling a friend that the president was “not only crazy but stupid.’’

In interviews, Barrack denied he said that, and insisted that many people miss Trump’s actual brilliance.

“POTUS has learned over time that Socratic testing and a lack of predictability is a worthy weapon in both negotiations and in keeping his team well-honed, unentitled, and on alert,’’ he said, using the initials for president of the United States.

“He has no truck with political correctness, self-promotion, or personal hubris of his team,’’ Barrack said.

“This may cause him to appear at times to be overly realistic, blunt, or to be politically insensitive even to his own subordinates. However, that is not the case.’’

Still, advisers to the president have at times expressed concerns. In private conversations over the last year, people who were new to Trump in the White House, which was most of the West Wing staff, have tried to process the president’s speaking style, his temper, his disinterest in formal briefings, his obsession with physical appearances, and his concern about the theatrics and excitement of his job.

In conversations with friends, Jared Kushner, the president’s son-in-law and senior adviser, has said Trump is “crazy but he’s a genius.’’