A once-secret U.S. military cyber operation launched during the last year of the Obama administration to disrupt Islamic State’s online presence underwent a delayed rollout due to interagency disagreements about the clandestine mission, according to newly released government documents and former U.S. officials.

Operation Glowing Symphony, initiated in late 2016, prompted at least one unidentified government agency to issue a formal “non-concur” opinion, disputing either the scope or necessity of the planned attack, according...