WASHINGTON — President Donald Trump tweeted early today that he is ordering a “major investigation” into voter fraud, revisiting unsubstantiated claims he’s made repeatedly about a rigged voting system.

The investigation, he said, will look at those registered to vote in more than one state, “those who are illegal and ... even, those registered to vote who are dead (and many for a long time).”

Depending on results, Trump tweeted, “we will strengthen up voting procedures!”

Trump has been fixated on 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.

His exaggerations about inauguration crowds and false assertions about illegal balloting have been distractions as advisers’ have tried to launch his presidency with a flurry of actions on the economy.

Trump’s 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.

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.

“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.

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.

Rep. Elijah Cummings, ranking Democrat on the House Oversight and Government Reform Committee, said today his panel has already sent letters to the attorneys general in all 50 states asking for reports of any election irregularities.

“The president can join me and my staff,” Cummings said on MSNBC.

He also said he wants Congress to restore voting protections, citing a Supreme Court ruling that “gutted” key sections of the Voting Rights Act, particularly the provision requiring southern states to get clearance in advance from the Justice Department before legislating changes in voting laws and procedures.

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 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.”