Some Republicans have also been critical. Nikki Haley, who ran against Ramaswamy for the Republican nomination for president in 2024, said “he’s a bad guy. It’s a shame he continues to get away with it”.

Vice-President JD Vance, when asked by the BBC at a press conference if he thought the ad was appropriate, did not say.

“It’s not really my concern,” Vance said. “What is my concern is who’s going to govern the next generation of American government.”

He also told the press conference he was “a little bit disgusted” by members of his own party who “are whining more about that advertisement than they are about what the congressional Democrats and other Democrats want to do to the United States of America”.

Speaking later at a rally in Ohio with Ramaswamy, Vance defended the Republican candidate, saying: “Vivek Ramaswamy had the audacity to run a TV commercial which calls it out like it is, and calls Amy Acton a liar.”

Political attacks ads are not a new feature of US politics, but David Lublin, a professor from American University’s School of Public Affairs, told the BBC that “they have become more intense, and the boundaries have stretched in terms of what one attacks about”.

Lublin said it was not new for relatives to be used against a political opponent, mentioning family members who testified against Robert F Kennedy Jr before he was confirmed as health secretary.

“But this is of a different order,” he said. “They’re estranged not over policy but over a rape allegation.”

Lublin believes President Donald Trump’s rhetoric and campaigns have helped act as a catalyst for the coarsening of American political discourse – mentioning when Trump mocked a reporter in Ohio who had a disability.

“We live in an age where certainly many candidates can appear mean and even inappropriate at times,” Lublin said, adding: “The key purpose of attack ads isn’t necessarily to convert the followers of your opponent, but more to depress their turnout.”

He expects the Ramaswamy attack ad to backfire, saying it could be an indication that his campaign is desperate to swing momentum in his favour in the increasingly competitive race for Ohio governor – even though a Democrat has not been elected governor there in over two decades.

Cook Political Report, a nonpartisan website that rates and tracks US elections, has moved the Ohio governor’s race from “leans Republican” to “toss up”, meaning neither candidate has a clear advantage.