“We do cheat,” Giuliani told “State of the Union” host Jake Tapper. “We have people who cheat in elections!”

“You're saying only Democrats cheat?” Tapper asked.

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“I've found very few situations where Republicans cheat,” Giuliani said, shrugging. “They don't control the inner cities the way Democrats do. Maybe if Republicans controlled the inner cities, they'd do as much cheating as Democrats.”

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“I think there are a lot of elections experts that would have very, very strong disagreements with you,” Tapper responded, shaking his head.

Several studies have shown that voter fraud rarely occurs in U.S. elections. A News21 investigative reporting project published in The Washington Post found that only 2,068 cases of alleged voter fraud had been reported since 2000, compared with the 146 million registered to vote in a 12-year span.

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In a separate study, Loyola Law School professor Justin Levitt found 241 potentially fraudulent ballots out of 1 billion ballots cast over a 14-year period.

Giuliani also tried to cast doubt on at least one woman who accused Trump of groping her on an airplane in the early 1980s. In the past week, multiple women have stepped forward to accuse Trump of making unwanted sexual advances toward them.

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Tapper asked whether Giuliani thought the women were lying.

“I would not say it that way. I believe Donald Trump,” Giuliani said. “I don't know about the nine women [who came forward last week] . . . I'd have to study each case to tell you that.”

Giuliani instead questioned the circumstances of the woman's account — by insinuating that such an incident could not have occurred in first class.

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“Some of these things appear to me on their face to be kind of untrue,” Giuliani said. “Fifteen minutes of groping in a first-class cabin of an airplane? It doesn't make sense. I've been in first class a lot, fortunately. Since I stopped being mayor, I can afford first class. You know, you see everything that goes on in first class.”

While Giuliani did not name her, he probably was referring to Jessica Leeds, who told the New York Times that she was seated next to Trump in a first-class cabin more than 30 years ago when he lifted the armrest and began groping her.

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According to Ms. Leeds, Mr. Trump grabbed her breasts and tried to put his hand up her skirt.

“He was like an octopus,” she said. “His hands were everywhere.” She fled to the back of the plane. “It was an assault,” she said.

The Times account did not specify the length of time Trump allegedly groped Leeds but stated she “quickly” fled the cabin afterward.

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Ms. Leeds was 38 at the time and living in Connecticut. She had been seated in coach. But a flight attendant invited her to take an empty seat in first class, she said. That seat was beside Mr. Trump, who did not yet own a fleet of private aircraft, records show. He introduced himself and shook her hand. They exchanged pleasantries, and Mr. Trump asked her if she was married. She was divorced, and told him so. Later, after their dinner trays were cleared, she said, Mr. Trump raised the armrest, moved toward her and began to grope her. Ms. Leeds said she recoiled. She quickly left the first-class cabin and returned to coach, she said.

Giuliani doubled down on his defense on Fox News later Sunday morning, saying the women accusing Trump were possibly doing so “for fame” or “for money.”

“First class 30 years ago was considerably more luxurious than it was today,” Giuliani said. “Only six to eight to 10 people — couldn't possibly have happened. It's on its face not true.”

Giuliani's comments on voter fraud supplemented those of former speaker of the House Newt Gingrich and Republican vice presidential nominee Mike Pence, who also hit the Sunday morning political-show circuit to defend Trump.

Gingrich accused the media of rigging the election on a national level on ABC's “This Week.”

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“This is not about election officials at the precinct level,” Gingrich told “This Week” host Martha Raddatz, who also co-moderated the second presidential debate last Sunday. “Without the unending, one-sided assault by the news media, Trump would be ahead by 15 points.”

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Meanwhile, Pence said on NBC that he and his running mate would “absolutely accept the results of the election” as “the will of the American people.”

Pence repeated that sentiment on CBS’s Face the Nation: “The peaceful transfer of power is a hallmark of American history.”

He made no reference to the investigation into voter fraud in his home state of Indiana, where he is governor.

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During both interviews, Pence framed Trump’s comments about a “rigged election” as a criticism of the news media bias against him, particularly the focus over the past week on several women's allegations of unwanted sexual advances by the businessman.

Pence said the news media has focused on “unsubstantiated allegations” against Trump while it “willfully ignored an avalanche of hard evidence of corruption” on Clinton’s part. He said emails from Clinton’s time as secretary of state and more recent WikiLeaks emails of her campaign staff show a pattern of “greed, corruption and pay to play politics.”

This post has been updated.