By Kevin Liptak and Dan Merica

CNN

WASHINGTON (CNN) -- President Donald Trump believes millions of votes were cast illegally in last year's election, White House press secretary Sean Spicer said on Tuesday, but he wouldn't provide any concrete evidence for the claim, which has long been debunked.

"The President does believe that, I think he's stated that before, and stated his concern of voter fraud and people voting illegally during the campaign and continues to maintain that belief based on studies and evidence people have brought to him," Spicer said.

Pressed for what evidence exists, Spicer would say only that Trump "has believed that for a while based on studies and information he has."

When pushed about whether Trump will call for an investigation into the voter fraud, Spicer said, "maybe we will."

Trump surprised the top Republicans and Democrats in Congress on Monday when, during a dinner at the White House, he repeated his claim that millions of undocumented immigrants voted for Hillary Clinton -- allegedly depriving him of the popular vote, according to two sources familiar with the meeting.

Trump lost the popular vote to Hillary Clinton by nearly 3 million votes in November, but won the Electoral College and thus the presidency. Trump, however, has seemingly been fixated on the popular vote, tweeting after the election in November that, "In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally."

A number of studies have found no evidence of widespread voter fraud.

The Truth About Voter Fraud, a report written by experts at The Brennan Center for Justice, found voter fraud rates were between 0.00004% and 0.0009%.

"Given this tiny incident rate for voter impersonation fraud, it is more likely that an American will be struck by lightning than that he will impersonate another voter at the polls," reads the report.

Trump's lawyers -- in an objection to Green Party candidate Jill Stein's Michigan recount petition -- have also argued that there was no evidence voter fraud in the 2016 election.

"All available evidence suggests that the 2016 general election was not tainted by fraud or mistake," the lawyers wrote in a filing.

South Carolina Republican Sen. Lindsey Graham slammed Trump earlier Tuesday over the claim.

"I wasn't there, but if the President of the United States is claiming that 3.5 million people voted illegally, that shakes confidence in our democracy --- he needs to disclose why he believes that," Graham told CNN.

Spicer said Tuesday that Trump believes in widespread voter fraud, in part, because of a study that found 14% of people who voted were non-citizens.

Spicer did not say expressly which study Trump has read, but a 2014 study by Jesse Richman and David Earnest found more than 14% of non-citizens in 2008 and 2010 "indicated that they were registered to vote."

The authors wrote, in a Washington Post opinion piece, the report showed "that 6.4 percent of non-citizens voted in 2008 and 2.2 percent of non-citizens voted in 2010."

The study was designed by Cooperative Congressional Election Study, and in 2014 the group said their sample was so small that it could be incorrect and attributable to normal survey error and not non-citizens saying that they are registered to vote.

Trump's campaign cited in October a 2012 study from the Pew Charitable Trusts entitled "Inaccurate, Costly and Inefficient: Evidence that American Voter Registration Systems Needs an Upgrade" as backup for that claim. The study found that "about 24 million voter registrations are no longer valid or are significantly inaccurate" and "more than 1.8 million dead people are listed as voters."

The study, which is based on 2011 data, is about the need to update voter rolls and underscores deficiencies in the voter registration system, but does not show that people who have registrations in two states are voting twice for Democrats or for Republicans.

David Becker, the primary author of the Pew Report, tweeted in November, "We found millions of out of date registration records due to people moving or dying, but found no evidence that voter fraud resulted."

CNN's Jennifer Agiesta contributed to this report.