The Trump administration says Attorney General Jeff Sessions was acting as a then-U.S. senator when he talked to Russia’s ambassador at an event during last year’s Republican National Convention in Cleveland, but Mr. Sessions paid for convention travel expenses out of his own political funds and he spoke about Donald Trump’s campaign at the event, according to a person at the event and campaign-finance records.

Mr. Sessions made comments related to Mr. Trump’s presidential campaign at a Heritage Foundation event during the...