The choir and orchestra that performed the song belonged to the First Baptist Church of Dallas, an evangelical church led by Pastor Robert Jeffress. The church co-sponsored the concert with the Salem Media Group, a media company that focuses on Christian and conservative content.

The original composition had verses that were left out of the July performance, said the song’s composer, Gary Moore, a former minister of music at the First Baptist Church of Dallas who now works at a baptist church in Houston.

Mr. Moore, 73, said he was surprised to see the song shared twice by the president on social media. He first composed it shortly after the November election, but he said the words “make America great again” were not only a reference to Mr. Trump.

They were also a tribute to the founding fathers’ respect for freedom of speech and freedom of religion, he said. “I think that’s what made our country great to begin with,” he said. “And I think we have to work to make it great every morning.”

The Kennedy Center event came on a day when Mr. Trump was particularly active on Twitter; he posted a flyer for the evening’s festivities in between criticizing the news media and insulting MSNBC morning show hosts Mika Brzezinski and Joe Scarborough.

On July 2, just after midnight, Mr. Trump tweeted a photograph of himself at the Kennedy Center and wrote that the United States would always take care of its veterans. Later that morning, he shared a video of himself wrestling and repeatedly punching a man with a CNN logo superimposed over his face.

Since he shared a video clip of the song, it has been re-tweeted more than 30,000 times by fans who praised the performance, and by critics who wondered why the president had not shared the national anthem instead.