Also registered to vote in two states was Trump’s daughter, Tiffany Trump, in New York and Pennsylvania.

Trump’s Treasury secretary nominee Steve Mnuchin also falls afoul of Trump’s definition of fraud, registered in New York and California.

While it is illegal to cast ballots in two states, it is not illegal to be registered in two states.

Bannon registered to vote in New York on October 14, 2016, and cast an absentee ballot there, according to New York City elections officials. At the time, he was also registered in Sarasota County, Florida, where he had been on the voter rolls since August 25, officials said.

Florida voting authorities cancelled Bannon’s registration Wednesday, the Associated Press reported.

Bannon’s Florida registration listed as his address the home of Andy Badolato, a friend of Bannon’s who has worked on some of his political documentary films and written for Breitbart News, the far-right website that Bannon controlled before entering the White House as chief strategist and senior counsellor to the president.

In a pair of tweets early on Wednesday morning, Trump decried dual-state registration.

“I will be asking for a major investigation into VOTER FRAUD, including those registered to vote in two states, those who are illegal and … even, those registered to vote who are dead (and many for a long time). Depending on results, we will strengthen up voting procedures!” the president wrote .

Trump’s statement followed the White House confirming on Tuesday that the president continues to believe the debunked theory that millions of people vote illegally in US elections. Trump has repeatedly blamed this for his loss of the national popular vote to Hillary Clinton, his Democratic opponent, by a margin of almost 3 million.

An intriguing hint of why Trump continues to believe this emerged from his remarks at a bipartisan luncheon held Monday, where he repeated his claim. Challenged, he backed it up with an anecdote featuring golfer Bernhard Langer, who Trump said recounted a frustrating experience when trying to vote near his Florida home on Election Day, the New York Times reported, citing people present at the luncheon.

The Times reported that Trump said part of Langer’s frustration was that “ahead of and behind [him in line] were voters who did not look as if they should be allowed to vote.”

A White House official “contradicted” that version of the depicted events, and told the Times that Trump had instead been telling a story relayed to the golfer by one of Mr Langer’s friends.

Langer is a German citizen and cannot vote in US elections.

Fellow Republican John McCain was among those pushing back against Trump’s claims. “Look, there’s no evidence of that and I think that those who allege that have to come up with some substantiation of the claim,” McCain said Wednesday on MSNBC’s Morning Joe.

A spokeswoman for Bannon did not immediately respond to a request for comment.

Those alleging voter fraud in US elections have long pointed to people still being registered to vote after they die and to those registered in two states as proof that such fraud exists or is possible, as White House press secretary Sean Spicer did Tuesday while being pressed for proof of Trump’s claims.

Spicer mentioned a 2012 Pew study that estimated that as much as 13 per cent of national voter registrations were inaccurate or invalid. But an author of that same study emphasised after Spicer’s briefing that this was simply faulty registrations - not voter fraud.

The author, David Becker, tweeted: “We found millions of out of date registration records due to people moving or dying, but found no evidence that voter fraud resulted.”

Becker’s study found that almost 2.7 million people appear to be registered in two states, and more than 70,000 people could be registered in three or more. In all, more than 2.75 million people appear to have multiple registrations, and more than 1.8 million dead people remain registered on voter rolls.

Additional reporting by Washington Post and Associated Press