PHILADELPHIA — Former New York City Mayor Rudolph Giuliani on Wednesday predicted that hackers could release incriminating emails from Hillary Clinton before the November election, or extort or threaten Mrs. Clinton if they decide to hang onto them.

“I would be surprised … if the Russians haven’t hacked all of Hillary’s emails way back when they were sitting in [a] garage,” Mr. Giuliani said. “That server of hers was less secure than the DNC server that was hacked — considerably less secure.”

Mr. Giuliani, speaking at a Republican National Committee event near the Democratic National Convention, was referring to the recent Democratic National Committee email hack in which the Clinton campaign has suggested Russia was involved.

“I would tell you there is no doubt our enemies did it,” he said. “If they can hack the DNC computer … there’s no question they hacked hers.”

“So those emails are being held by people,” Mr. Giuliani said. “They should be released before the election. If they’re not released before the election, they can be used to extort her. They could be used to influence her. They could be used to threaten her.”

“She did not destroy 35,000 emails because they contain notes to Chelsea about her dresses,” he said. “She destroyed 35,000 emails because they contain incriminating information.”

“I will guarantee you that those 35,000 emails contain incriminating information about connections between the Clinton Foundation and the hundreds of millions they were getting and all the favors she was doing as secretary of state while Bill Clinton was raking in the cash,” Mr. Giuliani said.

At a news conference earlier in the day, Republican presidential nominee Donald Trump said if Russia was behind the DNC hack, he hoped they also had Mrs. Clinton’s deleted emails. Mrs. Clinton’s campaign countered that Mr. Trump was actively encouraging espionage.

Mr. Giuliani said Mr. Trump meant that the emails should be released to law enforcement.

“I’m sure what he means is that they should be released to the FBI,” he said. “I’m sure that’s what he would do if he were in charge.”

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