WASHINGTON -- President Donald Trump, who once claimed the election would be rigged against him and has insisted against all evidence that millions of illegally cast ballots deprived him of receiving more votes than Hillary Clinton, called Wednesday for an investigation into voter fraud.

Trump made the announcement on Twitter.

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

even, those registered to vote who are dead (and many for a long time). Depending on results, we will strengthen up voting procedures! — Donald J. Trump (@realDonaldTrump) January 25, 2017

The Republican secretary of state in Ohio, a state Trump carried in November, quickly fired back.

We conducted a review 4 years ago in Ohio & already have a statewide review of 2016 election underway. Easy to vote, hard to cheat #Ohio https://t.co/OpDrPUX6Ev — Jon Husted (@JonHusted) January 25, 2017

The president of the Brennan Center for Justice at New York University Law School, Michael Waldman, expressed concern that the investigation could lead efforts to keep legitimate voters from the polls.

"The notion that millions of people voted illegally two months ago, and nobody noticed, is preposterous on its face," Waldman said. "An expensive investigation of imaginary voter fraud is not needed. It could easily devolve into a witch hunt. Worse, it could be used to justify sweeping voting restrictions."

A 2012 study by the Pew Center on the States' Election Initiatives found problems with 24 million voter registrations, such as not removing dead voters from the rolls or failing to remove the names of those who moved out of state and registered at their new homes.

"There is absolutely no connection between voter records being out of date and fraud," the study's author, David Becker, now executive director and cofounder of the Center for Election Innovation and Research in Washington, told NJ Advance Media in October.

Becker made similar comments after the election.

As primary author of the report the Trump camp cited today, I can confirm that report made no findings re: voter fraud. /1 — David Becker (@beckerdavidj) November 28, 2016

We found millions of out of date registration records due to people moving or dying, but found no evidence that voter fraud resulted. — David Becker (@beckerdavidj) November 28, 2016

Trump's call for an investigation came after he told congressional leaders Monday that 3 million to 5 million illegal votes were cast, more than the difference separating him from Clinton. It's a repeat of a claim made in November, and the White House has yet to produce evidence to back him up.

"The president does believe that," White House spokesman Sean Spicer told reporters Tuesday. "He has stated that before. I think he stated his concerns, voter fraud and people voting illegally, during the campaign."

During the third presidential debate, Trump refused to commit to accepting the election results.

Voting rights advocates criticized Trump's comments.

"The White House is bashing immigrants, undermining voting rights, and playing to bigotry all at once," said Wade Henderson, president and chief executive of the Leadership Conference on Civil and Human Rights, a coalition of civil rights organizations."

Before his inauguration, Trump criticized Rep. John Lewis (D-Ga.), a leader of the 1965 Selma to Montgomery, Ala., march that led to the passage of the Voting Rights Act.

He promised to nominate Supreme Court justices with views similar views to the late Antonin Scalia, who called the law a "perpetuation of racial entitlement." Trump's nominee for attorney general, U.S. Sen. Jeff Sessions (R-Ala.), said the Voting Rights Act was "a piece of intrusive legislation."

And during the campaign, Trump endorsed voter identification laws that federal courts have said prevent minorities from voting but Republicans have defended as necessary to prevent in-person voter fraud, which has been shown to be virtually non-existent.

Jonathan D. Salant may be reached at jsalant@njadvancemedia.com. Follow him on Twitter @JDSalant. Find NJ.com Politics on Facebook.