Israeli TV station Channel 12 reported Sunday that Prime Minister Benjamin Netanyahu had fallen out with army chief Eyal Zamir over an unspecified new directive on Iran.

Netanyahu and Defense Minister Israel Katz have both denied the reports, but a senior Israeli source with deep knowledge of the people involved has told CBS News the report of a rift seems credible.

The biggest tell, the source said, is that the Channel 12 report passed through military censorship. All stories by Israeli media that deal with national security must go through the censor before publication. This is key, according to the source, becaus...