WASHINGTON — President Donald Trump says he will order an investigation into voter fraud.

The president tweeted early Wednesday that the measures will affect 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).”

Trump says that “depending on results, we will strengthen up voting procedures.”

Trump repeatedly made disputable claims of a rigged voting system before the election, but now in the White House, he continues to raise concern over fraud.

I will be asking for a major investigation into VOTER FRAUD, including those registered to vote in two states, those who are illegal and….

— Donald J. Trump (@realDonaldTrump) January 25, 2017

He 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.

Writer Stephen Ohlemacher contributed to this report.