"They're trying to run out the clock," Giuliani told CNN. "They can have the investigation. The investigation will be after the debate, after the election is over. What they're trying to do is cover up this scandal as much as possible."
Giuliani went on to blast Vice President Biden for arguing, in last week's vice presidential debate, that the White House was unaware of requests to the State Department for additional security.
"Where the heck was he?" Giuliani said. "They were demanding more security. They were begging for more security."
The former mayor added that he believed "something funny's going on here."
"Something's rotten in the state of Denmark," he added.
Giuliani did agree that so far, the Romney campaign had not managed to get much political momentum from the issue — but added it could become a potent topic in the campaign.
"I think if, in fact, this becomes a question of the president's lack of leadership, then it cuts into the economy as well," Giuliani said. "It's beginning to become like that. The White House … has fumbled this — whether it's a deliberate cover-up or they're making it look like a cover-up, they have fumbled the ball four or five times here."
On Sunday, Obama adviser Robert Gibbs accused the Romney campaign of "playing politics with this issue."
"We don't need wing-tip cowboys," Gibbs said on CNN's "State of the Union" program. "We don't need shoot-from-the-hip diplomacy, and when Mitt Romney first responded to what was going on in Libya, his own party called him out for insensitivity."
Giuliani also said that Tuesday's town hall-style debate might make it difficult for the president to aggressively challenge Mitt Romney, as his campaign has promised.
"I don't know how aggressive you can get in a debate like that," Giuliani said. "Probably you're going to see a performance like Joe Biden. If that had been an audience thing, they'd have wondered what he was laughing at."