Senator Tim Kaine of Virginia on Sunday compared Donald J. Trump’s encouragement of Russia to hack Hillary Clinton’s emails to the Watergate scandal, which led to President Richard M. Nixon’s resignation.

Mr. Kaine, Mrs. Clinton’s running mate, made the remarks on ABC’s “This Week” while he was being questioned about Mrs. Clinton’s use of a private email server while she was secretary of state, an issue that has dogged her throughout her campaign.

Mr. Kaine used the moment to attack Mr. Trump’s refusal to release his income tax returns and to attack his comments this summer that Russia should make public anything they might have stolen from Mrs. Clinton’s emails, remarks he made in the wake of the disclosure that hackers had accessed emails from the Democratic National Committee.

“He has openly encouraged Russia to engage in cyberhacking to try to find more emails or materials, and we know that this cyberattack on the D.N.C. was likely done by Russia,” Mr. Kaine said of Mr. Trump on Sunday.