Two executives of Hong Kong pro-democracy newspaper Apple Daily, charged under a national security law, were denied bail on Saturday in a case that has drawn international condemnation and stoked fears over media freedoms in the financial hub.

Editor-in-chief Ryan Law, 47, and chief executive officer Cheung Kim-hung, 59, were among five Apple Daily executives arrested on Thursday when 500 police also raided the outlet's newsroom, which authorities described as a "crime scene."...