Anthony Scaramucci was almost finished with one of his three Sunday television talk show appearances when he started speaking directly to one particular viewer at home.

“If I said some things about him when I was working for another candidate, Mr. Trump, Mr. President, I apologize for that. Can we move on off of that?” Mr. Scaramucci, the new White House communications director, said on CNN’s “State of the Union.” “I know you and I have moved on off of that,” he added, before commenting that the host, Jake Tapper, “hasn’t moved on off of that, obviously.”

Mr. Tapper laughed. Mr. Scaramucci continued. “I’m going to be working for you,” he told the president via television. “And I’m going to serve the American people. And we’re going to get your agenda out into the heartland, where it belongs.”

Mr. Tapper replied, “I love how you’re talking to one specific viewer right now.”

Mr. Scaramucci, the hedge fund investor-turned-message strategist, went on his first official television outing on Sunday. It was an unusually high-stakes rollout for a communications director because Mr. Scaramucci knew his boss would be taking notes. And it came the weekend before Mr. Trump’s son and son-in-law are scheduled to appear before congressional committees investigating possible collusion between the Trump campaign and Russian officials.