WASHINGTON (AP) — Donald Trump holds the most powerful office in the world. But he's dogged by insecurity over his loss of the popular vote in the election and a persistent frustration that the legitimacy of his presidency is being challenged by Democrats and the media, aides and associates say.

Trump's fixation has been a drag on the momentum of his opening days in office, with his exaggerations about inauguration crowds and false assertions about illegal balloting intruding on advisers' plans to launch his presidency with a flurry of actions on the economy. His spokesman Sean Spicer has twice stepped into the fray himself, including on Tuesday, when he doubled down on Trump's false claim that he lost the popular vote because 3 million to 5 million people living in the U.S. illegally cast ballots.

"He believes what he believes based on the information he was provided," said Spicer, who provided no evidence to back up the president's statements. All 50 states and the District of Columbia have finalized their election results with no reports of the kind of widespread fraud that Trump is alleging.

If the president's claim were true it would mark the most significant election fraud in U.S. history — and ironically, would raise the same questions about Trump's legitimacy that he's trying to avoid. Yet Spicer repeatedly sidestepped questions about whether the Trump administration would investigate the allegations pushed by the president.

"Anything is possible," he said.

Some Trump allies say Trump is justified in using his platform to defend his standing. They point to Georgia Democratic Rep. John Lewis' pre-inauguration statement that he did not see Trump as a legitimate president, as well as U.S. intelligence agencies' assessment that Russia meddled in the election in order to help Trump win.

"Segments of his own government keep driving this narrative," said Roger Stone, a longtime confidant. "I don't think it hurts to point it out."

Key advisers in Trump's inner circle concede the focus on crowd claims and alleged voter fraud have been a distraction. But who's going to stop him from airing his complaints?

After relishing in Friday's inaugural festivities, the new president grew increasingly upset the next day by what he felt was "biased" media coverage of women's marches across the globe protesting his election, according to a person familiar with his thinking. Trump was particularly enraged with CNN, which he thought was "gloating" by continually running photos of the women's march alongside the smaller crowds that attended his inauguration the day before, according to this person, one of several White House aides and associates who spoke on the condition of anonymity because they were not authorized to speak publicly about private conversations.

Tuesday night on Twitter, Trump slammed CNN again, referring to the network as "FAKE NEWS @CNN" while praising rival Fox News Channel.

Trump has had a tumultuous relationship with the press, frequently calling the media dishonest and insulting individual reporters by name at his rallies and on Twitter. Still, two people close to Trump said he expected his coverage to turn more favorable once he took office. Instead, he's told people he believes it's gotten worse.

The bad press over the weekend has not allowed Trump to "enjoy" the White House as he feels he deserves, according to one person who has spoken with him.

The result has been a full display of Trump's propensity for exaggeration and more. During an appearance at the CIA Saturday, he wrongly said the inaugural crowds gathered on the National Mall stretched to the Washington Monument, despite clear photo evidence to the contrary. And during a reception with lawmakers from both parties Monday night, he repeated his false assertion that millions of illegal immigrants provided Hillary Clinton's margin in the popular vote.

It's not the first time that Trump, who is known to be both thin-skinned and dedicated to polishing his public image, has become fixated on details that challenge his success. When journalist Timothy O'Brien wrote in a 2005 book that Trump was a multimillionaire, not a billionaire, the real estate mogul sued him for $5 billion. The case was dismissed. Trump appealed, accusing the journalist of libel. He lost that, too.

Spicer hinted at Trump's feelings during his maiden press briefing on Monday.

"There is this constant theme to undercut the enormous support that he has," Spicer said. "And I think that it's just unbelievably frustrating when you're continually told it's not big enough, it's not good enough, you can't win."

Less than one week into the administration, Spicer has twice been sent to the White House briefing room to reiterate his boss' message. Trump is said to have approved of Spicer's angry tirade against the media on Saturday, which included false statements about the size of inaugural crowds. But the president, who is intensely focused on optics, was said to be critical of Spicer's on-camera image.

By Monday, Spicer was donning a darker suit and his lectern in the briefing room had been lowered somewhat.

Underscoring Trump's habit of stoking rivalries among his staff, he has told people he wants his counselor, Kellyanne Conway, to be on television more. He cheered her use of the phrase "alternative facts" in a recent interview as a way to counteract what he believes is the media's inherent bias.

Those around Trump are trying to get the cable news consumer-in-chief to be near a television less often, according to one person who has spoken with him.

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AP writer Stephen Ohlemacher contributed to this report.

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