At a moment when Mrs. Clinton and the Obama administration have warned that Russia is trying to influence the American election, the mysterious release of the tape is also certain to raise new questions about the scope of attacks on the Democratic National Committee and the Clinton campaign.

A former Defense Department official present at the fund-raiser, Andrew C. Weber, who raised the question about nuclear modernization, verified the contents of the tape, but also suggested its release was part of the same hacking campaign that exposed D.N.C. emails.

Before she turned to nuclear matters, Mrs. Clinton used the fund-raiser to suggest that she would be much firmer against foreign nations that hack into American networks. Though the administration never formally accused China of stealing the security-review records of nearly 22 million federal employees and contractors, she called the theft “a gold mine for Chinese intelligence.”

“They are at it all the time,” she said of the Chinese state-sponsored hackers. But she also seemed to suggest — more directly than she did in Monday night’s debate — that she thinks the best deterrent to the Russians, the Chinese, the Iranians and the North Koreans, all of whom she named, was a dose of American offensive cyberweaponry.

“They have physical assets that are also connected on the internet,” she said. “So they have to know we would retaliate. So that provides a certain level of deterrence.”