“You’re threatening me in the Rose Garden,” Mr. Gorka bellowed at Mr. Karem, who had challenged him to take it outside. “You’re not a journalist. You’re a punk.”

A chant of “Gorka! Gorka! Gorka!” broke out among the other social media activists, while Joy Villa, a singer-songwriter and Trump supporter, who was resplendent in a floor-length red, white and blue gown emblazoned with the word “Freedom,” laughed and declared, “Fake news is over!”

The fracas was filmed by James O’Keefe, who uses undercover videos to embarrass journalists and liberal political figures.

Historically, presidents have used the Rose Garden to dignify important moments. John F. Kennedy welcomed the Mercury astronauts there; Richard M. Nixon had his daughter Patricia’s wedding there. Mr. Trump is the first to turn the garden into a well-manicured mosh pit. Rather than telling his guests to watch their manners, the president scored the slugfest like a referee.