Television talk shows play a formative role in shaping public debate in Egypt, and Egyptian intelligence services often brief the presenters of the programs about messages to convey to the public. The hosts typically prefer to characterize the conversations as journalists talking to sources.

In addition to the call with Mr. Megahed, three other audio recordings of strikingly similar telephone conversations with the same intelligence agent, Captain Kholi, were all provided to The Times by an intermediary supportive of the Palestinian cause and opposed to President Sisi. The origin of the recordings could not be determined.

Mr. Megahed, in an interview, said that he had agreed with Captain Kholi based on his personal assessment of the need to avoid a fresh outbreak of violence, not on the orders of the intelligence service.

“I am friends with Ashraf and we talk all the time,” Mr. Megahed said. “Another intifada would be bad. I have no problem saying all of the things you have heard in that call in public.”

As for those who disagreed, he said, “We should have buses pick up all the people who say they want to go fight for Jerusalem and actually drive them to Jerusalem. Go fight if you are so tough. People are sick of the slogans and all that. I only care about the interests of my country.”

Two of the calls were with other well-known Egyptian talk show hosts. One of them, Mofid Fawzy, quickly denied taking part in any such conversation and immediately hung up the phone.