"I'm sorry, dead people generally vote for Democrats rather than Republicans," the former New York City mayor told CNN's Jake Tapper on "State of the Union." "You want me to (say) that I think the election in Philadelphia and Chicago is going to be fair? I would have to be a moron to say that."
But he did say the amount of cheating would only impact extremely close races -- noting, for example, if either Trump or Hillary Clinton won Pennsylvania by "5 points," the cheating he alleges would occur would be negligible and not change the outcome.
Giuliani was backing up Trump, the Republican nominee, who has repeatedly claimed on the campaign trail -- without providing evidence -- that his race against Clinton is being rigged.
Trump tweeted Sunday: "The election is absolutely being rigged by the dishonest and distorted media pushing Crooked Hillary - but also at many polling places - SAD"
But Pence told NBC's Chuck Todd on "Meet the Press" that he will accept the Election Day results.
"We will absolutely accept the result of the election," he said. "Look, the American people will speak in an election that will culminate on November the 8. But the American people are tired of the obvious bias in the national media. That's where the sense of a rigged election goes here, Chuck."
Tapper pushed back on Giuliani, saying even Republicans had debunked the conspiracy theories pushed online that low vote totals in Philadelphia in 2012 for Mitt Romney were the result of a rigged process.
Giuliani said as a prosecutor, he remembers an election in Chicago in which 720 supposedly dead people voted -- and that 60 dead people cast ballots in his own mayor's race.
He said elections fraud would only make a difference in a 1 to 2 percentage point races.
He also said that only Democrats do it, because it happens in inner cities.
"I can't sit here and tell you that they don't cheat. And I know that because they control the polling places in these areas. There are no Republicans, and it's very hard to get people there who will challenge votes. So what they do is, they leave dead people on the rolls and then they pay people to vote as dead people, four, five, six, seven" times, Giuliani said.
"I've found very few situations where Republicans cheat. 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 do," he said.
Tapper said: "I think there are a lot of elections experts that would have very, very strong disagreements with you."
Giuliani responded: "Well then they never prosecuted elections fraud."
Newt Gingrich, the former House speaker and also a top Trump ally, said on ABC's "This Week" that Trump's concerns about election rigging are "not about election officials at the precinct level."
However, he also urged Trump voters to monitor polling stations.
"I remember when Richard Nixon had the election stolen in 1960, and no serious historian doubts that Illinois and Texas were stolen. So to suggest that, we have, you don't have theft in Philadelphia is to deny reality," Gingrich said.