With just four weeks until the election, Donald J. Trump and Republican candidates nationwide are putting transgender issues at the center of their campaigns, tapping into fears about transgender women and girls in sports and about taxpayer-funded gender transitions in prisons.

Since the beginning of August, Republicans have poured more than $65 million into television ads in more than a dozen states on these topics in some of the country’s most competitive races, according to a New York Times analysis of advertising data compiled by AdImpact.

The flood of ads in races for the House, Senate and White House inflame cultural divisions and cast Democrats as outside the mainstream. They are a sign that Republican strategists believe they have found a potent third leg for their messaging stool in 2024, along with the mainstays of inflation and immigration.

Republicans are returning to a message that was tried, mostly unsuccessfully, in the 2022 midterms, as they attempt to motivate their base and curb their losses with female voters repelled by the party’s stance on abortion.

Mr. Trump’s most aired ad about Vice President Kamala Harris in recent weeks ends with the tagline: “Kamala is for they/them. President Trump is for you.”

In Ohio since the start of September, every ad about Senator Sherrod Brown from the leading Senate Republican super PAC has touched on transgender topics, such as accusing him of “allowing transgender biological males in girls’ sports.” Mr. Brown is one of the nation’s most vulnerable Democratic incumbents.