"The Chinese have to look very carefully at the steps they take because people in America remember Tiananmen Square, they remember the picture of the man standing in front of the line of tanks," Bolton said in an interview with VOA News published Thursday.
Chinese forces crushed protests at Beijing's Tiananmen Square in 1989 -- an event immortalized in an image of an unarmed man facing down tanks.
"It would be a big mistake to create a new memory like that in Hong Kong," Bolton said.
Demonstrators in Hong Kong have staged 10 weeks of relentless protests to demand greater freedoms, and there are growing concerns that Beijing is considering direct intervention in the crisis.
US President Donald Trump on Thursday said that a meeting between Chinese leader Xi Jinping and Hong Kong's pro-democracy activists could lead to a "happy" ending to demonstrations.