Ohio Gov. John Kasich might not be an active candidate for president anymore. But his team still wants supporters to know that Mr. Kasich is outperforming presumptive GOP presidential nominee Donald Trump in key battleground states.

John Weaver, chief strategist for Mr. Kasich’s 2016 presidential campaign, on Wednesday touted polling released by Ballotpedia that showed likely Democratic presidential nominee Hillary Clinton beating Mr. Trump in Florida, Iowa, Michigan, North Carolina, Ohio, Pennsylvania and Virginia by an average of 11 points.

Mr. Weaver went on to write that Mr. Kasich led Mrs. Clinton by an average of 4 points in the seven battleground states, while House Speaker Paul D. Ryan tied her.

“The results get even more interesting when they modeled what the election will look like in November,” Mr. Weaver wrote. “Under a modeled electorate, Trump loses every swing state by 6-12 points. Governor Kasich wins 6 out of 7 swing states. Speaker Ryan wins 2 out of 7 swing states.”

“This data is just further proof that Governor Kasich is the most popular Republican politician in the nation today, and it underlines why his efforts to help our U.S. Senate and House candidates are so very important,” Mr. Weaver wrote.

The pitch from Mr. Weaver comes as some GOP delegates hold onto last-ditch hopes of leveraging party rules to deny Mr. Trump the Republican nomination at the GOP convention next month in Mr. Kasich’s home state — a push that both Mr. Trump and the Republican National Committee have dismissed.

Mr. Kasich dropped out of the 2016 race the day after the May 3 Indiana primary. He has yet to officially endorse Mr. Trump.

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