The chairwoman of the Federal Election Commission (FEC) is demanding that President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE either provide evidence to support his claim that he would have won New Hampshire's electoral votes in 2016 if not for voter fraud, or cease mentioning the claim.

Chairwoman Ellen Weintraub, a Democrat, wrote in a letter to the president reported by CNN that Trump risks "undermining the faith" of the American electorate in the fairness of U.S. elections.

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"Your voter-fraud allegations run the risk of undermining that faith," she wrote, according to CNN.

"To put in terms a former casino operator should understand," Weintraub added, "there comes a time when you need to lay your cards on the table or fold."

Weintraub's letter to the White House came a day after the president told supporters at a New Hampshire campaign rally that it wasn't their "fault" that he had lost the state in 2016, while insinuating that the state had been "taken" from his campaign.

Trump said "we should have won" New Hampshire, asserting, "It was taken away from us" and telling audience members that it was "not your fault."

Trump was edged out in 2016 in the state by former Secretary of State Hillary Clinton Hillary Diane Rodham ClintonBloomberg rolls out M ad buy to boost Biden in Florida Hillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Trump pledges to make Juneteenth a federal holiday, designate KKK a terrorist group in pitch to Black voters MORE (D), who won the state by a few thousand votes.

The president has long alleged that he would have won the national popular vote against Clinton in 2016 had it not been for millions of illegal votes, a baseless claim that led to the formation of a short-lived voter fraud commission headed by Vice President Pence and former Kansas Secretary of State Kris Kobach (R).