“The revolution has dismantled all the shackles that were present — not just for us, not just for the military, but for the entire state,” he says at another point. “The rules and the shackles were dismantled, and they are being rearranged.”

The officers’ winter uniforms and references to last December’s constitutional referendum suggest the meeting took place around that time. But the conversation foreshadowed the broad media crackdown that has played out since the military takeover. The new government has shut down Islamist television networks and the main newspaper supporting Mr. Morsi, and the police have arrested several journalists perceived as critical of the government or the military. And for whatever reason, privately owned newspapers and satellite networks now resound with cheers for the army and demonization of its Islamist opponents, just as the officers hoped.

The leak of the video, though, may raise different alarms. The clip was one of several snippets of the same meeting released Wednesday night and Thursday by RNN, an Islamist Web site, and in an interview, its acting director, Amr Farrag, said the material was obtained from “sources inside the military.” Military officials said Thursday that the army was starting an investigation.

Analysts said the video offered insights into motivations that might have helped propel the military’s takeover. “It betrays a real fear of what democratic discourse might look like and what that would mean for the military, in terms of what might be talked about and what might be exposed,” said Michael Wahid Hanna, a researcher on Egypt at the Century Foundation in New York.

The officers’ thin skin about the loss of the military’s “red lines,” he argued, is symptomatic of a much deeper worry. “If the military can be talked about in these unprecedented ways, the concern is that it erodes the stature of the military in the public imagination, and then the role of the military as an institution is potentially under threat.”