WASHINGTON—President Donald Trump reiterated his stance that the election of Democrat Doug Jones to an Alabama Senate seat would mark a serious blow to the Republican agenda, while not explicitly saying he backed GOP nominee Roy Moore, who faces allegations of sexual misconduct with teenagers several decades ago.

“The last thing we need in Alabama and the U.S. Senate is a Schumer/Pelosi puppet,” said Mr. Trump Sunday on Twitter, referencing Democratic leaders Sen. Chuck Schumer of New York and Rep. Nancy Pelosi of California....