Even as Donald J. Trump is trying to distance himself from the Heritage Foundation-led Project 2025, his running mate’s contribution to a new book by the project’s principal architect is complicating his efforts.

“Dawn’s Early Light,” a forthcoming book by the Heritage Foundation’s president, Kevin D. Roberts, calling for a “second American Revolution,” features a foreword by Senator JD Vance, the Ohio Republican whom Mr. Trump tapped as his running mate in July.

“In the fights that lay ahead, these ideas are an essential weapon,” Mr. Vance writes in his introduction, which was obtained and published online by The New Republic on Tuesday. The book is set for publication in September.

Mr. Vance announced in June that he had written the foreword for Mr. Roberts, whose think tank became an influential bastion of conservative policymaking during Ronald Reagan’s presidency and enjoyed exceptional influence during Mr. Trump’s time in office, providing a staffing pipeline for his administration.

But Mr. Vance’s endorsement of the book became more politically fraught after Mr. Trump publicly disavowed Project 2025, a set of sweeping policy proposals for a hoped-for Republican presidency that the think tank began preparing more than two years ago under Mr. Roberts’s direction. The project, which has been billed by Heritage as an attack on the “deep state” and proposes disbanding multiple federal agencies, excluding abortion from health care and ending an array of climate change programs, has become a popular target for Democrats.

Will Martin, a spokesman for Mr. Vance, wrote in an email Wednesday that “the foreword has nothing to do with Project 2025.” Mr. Vance “has plenty of disagreements with what they’re calling for,” Mr. Martin wrote, adding: “Only President Trump will set the policy agenda for the next administration.”