WASHINGTON—Attorney General William Barr escalated his criticism of the Federal Bureau of Investigation’s probe into possible Trump campaign connections to Russia, calling it a “travesty” that was opened on flimsy evidence.

Speaking at The Wall Street Journal CEO Council gathering on Tuesday, Mr. Barr said it was too soon to determine whether political bias motivated the inquiry, even after the Justice Department’s inspector general said he had found no evidence that FBI leaders acted out of partisanship.

John...