No public evidence has emerged of large-scale illegal voting in the November election, and Trump and the White House have failed to substantiate the president's claim, which he repeated this week.
Trump's own lawyers have stated in legal filings that there was no evidence of fraud in the November 8 election.
Even as major US media branded Trump's allegation an outright lie and lawmakers urged him to drop the subject, the president stuck to his guns on Wednesday.
"Depending on the results we will strengthen up voting procedures!" Trump added.
Trump has dwelled at length on the results of an election he won, against all expectations.
He argues that were it not for illegal immigrants voting, he would have won not just the state-weighted electoral college but also the popular vote, which was taken by Democratic opponent Hillary Clinton by around 2.9 million votes.
"I think the president has believed that for a while based on studies and information he has," Spicer said.
If proven, it would be an enormous political scandal.
Spicer said the Republican president nonetheless had confidence in the election outcome.
The president has previously cited a Pew report from 2012 that concluded more than "1.8 million deceased individuals are listed as voters."
That report provided no evidence to support Trump's claim, first made in October, that "people that have died 10 years ago are still voting," or that others voted in their name.
Trump has also cited an Old Dominion University study which suggested 14 percent of non-citizens said they were registered to vote.
But that study has been dismissed as having flawed methodology, with a sample size of under 1,000 and no link between being registered to vote and actually voting.
Even Trump's lawyers have stated there is no evidence of fraud in the 2016 election.
In a filing late last year against Green Party candidate Jill Stein's efforts to force a recount of votes in Michigan, they wrote: "All evidence suggests that the 2016 general election was not tainted by fraud or mistake.
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