Disinformation and political experts have raised concerns that such deceptive audio, known as a deepfake, could become prevalent this election season. Last year, the Republican National Committee used the technology to generate a video with images of doomsday scenarios after Mr. Biden announced his re-election bid. Gov. Ron DeSantis of Florida posted fake images of former President Donald J. Trump, his political rival, with Dr. Anthony Fauci, the former health official.

State lawmakers are scrambling to draft bills to regulate political content produced by artificial intelligence, which has already been used in tight foreign elections to mislead voters.

“The political deepfake moment is here,” Robert Weissman, the president of the progressive watchdog group Public Citizen, said in a statement. “Policymakers must rush to put in place protections or we’re facing electoral chaos.”

In New Hampshire, the attorney general’s office began investigating the robocall accusations following a complaint from Kathleen Sullivan, a former chairwoman of the state Democratic Party. In her complaint, Ms. Sullivan said that recipients of the unauthorized robocalls saw her husband’s name in their caller ID and were given her personal cellphone number to call to request removal from the call list.

Ms. Sullivan, the treasurer of a political committee pushing voters to write in Mr. Biden’s name on Tuesday’s ballot, wrote in her complaint that “these kinds of tactics, if left unpunished, will only get worse in the future.”