Mr. Fleischer said, “He’s just doing more of what President Obama successfully did, and what I’m fascinated about is, what does this mean for the future?”

On Monday, the president-elect met privately with television executives in a confidential session that was described later as a sometimes contentious effort to clear the air after a campaign season in which Mr. Trump often clashed with members of the media.

Mr. Trump is also scheduled to meet with editors and reporters at The New York Times on Tuesday.

But his decision to deliver a highly scripted video message suggests that he, like Mr. Obama, is eager to embrace new media opportunities. By Monday, Mr. Trump’s @RealDonaldTrump Twitter account, which he enjoys using, had 15.7 million followers. Once in the White House, he will inherit @POTUS, with its 12.1 million online followers.

Mr. Trump also spent Monday at his office in Trump Tower, interviewing a stream of potential Republican cabinet candidates. They included Rick Perry, a former governor of Texas; former Senator Scott Brown of Massachusetts; and Representative Tulsi Gabbard of Hawaii, a Democrat.

Perhaps the most interesting thing about Mr. Trump’s video was what he did not say in it.

On immigration, he avoided any mention of his plan to build a wall along the border with Mexico or his desire to deport immigrants here illegally, whether or not they have a criminal record. He made no mention of ending President Obama’s program that grants work permits to immigrants who were brought illegally to the United States as children.

Instead, Mr. Trump simply promised to direct the Labor Department to investigate visa abuses.

The tough-talking president-elect, who has often railed against Mr. Obama and “the generals” for what he often called their “stupid” conduct of foreign policy, said nothing in the video about fighting terrorism, confronting Russian aggression or pressuring NATO allies to pay more for their common defense.