WASHINGTON—The Justice Department backed Treasury Secretary Steven Mnuchin’s refusal to turn over President Trump’s tax returns to the House Ways and Means Committee.

In a 33-page opinion released late Friday, the Office of Legal Counsel wrote that Mr. Mnuchin reasonably concluded that he couldn’t satisfy the request from Rep. Richard Neal (D., Mass), the committee chairman. The memo argues that the request was really designed to make the returns public, not to oversee the performance of the Internal Revenue Service.

“Treasury...