HONG KONG—Thousands of antigovernment protesters in Hong Kong marched from a historic clock tower through a shopping district lined with luxury stores on Saturday, in a demonstration that some hoped would show President Trump the movement still has momentum.

After a meeting with China’s vice premier at the White House on Friday, Mr. Trump said the protests have “toned down a lot” and that “great progress has been made by China in Hong Kong.” He added that the situation is “going to take care of itself.”

The...