Colonial Japanese rule on occupied territories has been described as harsh as has been their treatment of prisoners of war. In some cases, this was not a fleeting occupation but one lasting years or decades (e.g., Korea, Taiwan, or Manchuria). Surely, not all of the people in these areas agreed with this treatment and there must have been measures to enforce Japanese laws. There are many parallels drawn with their allies in Nazi Germany. Was there a Japanese equivalent of the Gestapo (or Secret Police)? Did they operate in the Japanese home islands or only in colonial territories?
Yes, that would be the Kenpeitai. It was a military police corps, founded in 1881. The kenpeitai had jurisdiction everywhere within the Japanese empire and their conquered territories.
Although it was a military police corps, everyone fell under their jurisdiction. Not just the military, civilians as well.
The naval equivalent was the Tokkeitai. Both units acted uniformed and in plain clothes. They were both known for their very harsh and brutal treatment of their victims. Both units were disbanded in august 1945.
The kenpeitai was much larger and under control of the army. The tokkeitai was smaller, under control of the navy, but just as brutal. Both were used by the military governments as an instrument of terror on their own population.
added: I think KeMpeitai, with an m, is correct. However, I don't speak Japanese. That's why I stick with Wikipedia's transcription of the name.