The relatives of 10 people shot over three days in 1971 called on Charles to apologise for the actions of his men due to his role as Colonel-in-Chief of the Paras.
An inquest being held into the shootings - known as the Ballymurphy Massacre - is expected to hear evidence from former members of the regiment on Wednesday.
The families staged a protest near Laganside Courts in Belfast, where the inquest is being held, against the royal visit and held placards including one which read "Colonel in Chief of Paras Shame On You".
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John Teggart, a spokesman for the families, read a statement on their behalf during the demonstration.
He said: "Prince Charles is the Colonel-in-Chief of the Parachute Regiment and he must take full responsibility for the actions of his troops.
"We think that the timing of this visit is very insensitive given the evidence of mass murder and sheer brutality being described in court by witnesses over the past months.
"Charles should know the hurt families like ourselves are going though at this present time. This hurt is not restricted to us; we know that other families suffer as we d