The monarch is making a four-day visit to Kenya from tomorrow and says he will try to learn more about the wrongs people suffered there.
The rights group said it expected an unequivocal public apology from the king.
Ten years ago, the British government formally recognised that torture at the hands of the colonial administrators had taken place.
It expressed its sincere regret and agreed to pay compensation to thousands of veterans of the uprising.
More than 10,000 were killed when the British authorities suppressed a pro-independence movement in the 1950s – 1,000 were hanged after summary trials.