They held a news conference Sunday afternoon at ground zero to voice their opposition.
The families are also speaking out against what they call the "desecration" of the remains of victims of the terrorist attacks on the Pentagon and the crash at Shanksville, Pa.
Earlier this week, military officials revealed that partial remains of several victims were incinerated by a military contractor and sent to a landfill.
The disclosure came in a report by an independent panel that studied underlying management flaws at Dover Air Force Base mortuary in Delaware.
The families are calling for congressional hearings on ethical handling of remains.
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