2 Unsubstantiated Claims Made by Trump Since He Became President He made unsubstantiated claims during the campaign as well.

 -- Donald Trump made multiple unsubstantiated claims during the presidential campaign, and he has not stopped doing so since he assumed the presidency.

Trump is five days into his term, and there have been at least two times he made statements that have not been backed up by any evidence.

The first was one about the size of the crowd at his inauguration — a topic that has raised questions for White House press secretary Sean Spicer as well. The second relates to unproved allegations of voter fraud, which he has stated before.

Trump Makes Unproved Claims About Inauguration Audience

The question of how many people attended Trump's inauguration ceremony in person on Friday has been a hotly debated topic since it unfolded after a photo of the National Mall from the vantage point of the Washington Monument was compared with one of Barack Obama's first inauguration in 2009. The photos show the crowds gathered on the Mall as the inaugurations were underway.

No official crowd counts were released because the National Park Service, which oversees the Mall, does not provide them.

That didn't stop Trump from making his own estimates and sharing them when he went to CIA headquarters to speak to members of the intelligence community the next day.

"We had, it looked, honestly, looked like a million and half people, whatever it was. But it went all the way back, to the back of the Washington Monument, and by mistake, I get this network [on TV], and it showed you an empty field, and it said we drew 250,000 people. Now, that's not bad, but it’s a lie. We had 250,000 people literally around in the little bowl that we constructed," Trump said.

In his press briefing on Monday, Spicer defended his earlier claim that it was the most-watched inauguration ever, based on the number of people who watched it unfold in person, online, on television and through streaming services. That total has not been tabulated.

Trump Repeats His Unproved Claims That There Were Millions of Cases of Illegal Voting

During his first meeting with congressional leaders in the White House after his inauguration, Trump reportedly spent several minutes talking about the election results. Democratic and Republican sources familiar with the conversation told ABC News that as part of that discussion, Trump said that he lost the popular vote because of millions of illegal votes.

He specifically said that "3 to 5 million illegals" voted, according to two Democratic aides who spoke on condition of anonymity. A Republican House aide corroborated the account, but said the comments were made in jest during a jovial exchange with House Minority Leader Nancy Pelosi of California.

Today, House Speaker Paul Ryan was asked at a news conference about what Trump said, and Ryan responded that he did not want to get into a discussion on the topic but reiterated that he has not seen anything to back Trump's claim.

"I have seen no evidence to that effect. I have made that very, very clear," said Ryan, R-Wis.

Spicer was pressed on the question of voter fraud during today's press briefing and doubled down, calling it a "long-standing belief" that Trump holds.

"He continues to maintain that belief based on studies and evidence people have presented to him," Spicer said of Trump.

Spicer told reporters today that "maybe we will" launch an investigation into Trump's claims.

"Anything's possible, I think, at some point," he added. "There is no investigation. I said it was possible. Anything is possible. It was a hypothetical question."

This is not the first time that Trump has made this unsubstantiated claim. After he became president-elect, he posted at least two tweets about "serious voter fraud" and "millions of people who voted illegally."

Hillary Clinton won the popular vote by nearly 3 million ballots.

In December, Mike Pence, the vice-president-elect at the time, defended Trump, citing a Pew study as the source of his numbers.

But the Pew study's primary author, David Becker, tweeted in response to references to his research, "As primary author of the report the Trump camp cited today, I can confirm the report made no findings re: voter fraud. We found millions of out of date registration records due to people moving or dying, but found no evidence that voter fraud resulted. Voter lists are much more accurate now than when we issued that study in 2012, thanks to the 20 states sharing data through @ericstates_info."

In another tweet as president-elect, Trump wrote that there was "serious voter fraud in Virginia, New Hampshire and California." There is no evidence to back up the claim, and it's unclear why he singled out those states.

ABC News reached out to election officials in all 50 states shortly before Election Day, and none had any evidence or reason to believe that widespread voter fraud occurred or would occur in their states.

ABC News' Devin Dwyer and MaryAlice Parks contributed to this report.