The relatives said that the plan to house the remains underground in the same building as the National September 11 Memorial Museum is disrespectful and that they would rather see the remains entombed aboveground on the adjacent memorial plaza.
"Let us have a voice! Let us have a say!" said retired firefighter Jim Riches, who lost his son, also a firefighter, in the 2001 terrorist attacks. "We are outraged, and we will never rest until our loved ones, America's heroes, rest in peace."
Sally Regenhard, who also lost her firefighter son at the World Trade Center, said the family members dread the opening of the museum on May 21.
"It's a day of sadness and a day of outrage," she said.
Not all family members agree. Other victims' families have been forthcoming about their support of the plan, saying the repository is a fitting site for the remains.
"It will show the world the way we treat our dead," Lee Ielpi, who lost his son in the attacks, said earlier in the week. "Let's get them back to the site."
The unidentified remains will be moved on Saturday from the medical examiner's office on Manhattan's East Side to the memorial site in lower Manhattan. City officials say that once there, the remains will be placed in a custom-designed repository at bedrock level in the same building as the museum. The remains will be moved in a solemn procession led by police and fire department vehicles.
The repository will be overseen by the medical examiner with hopes that improvements in technology could eventually help identify the 7,930 body parts.
City officials have said that family members were consulted about the plan, but the opponents say all relatives should have been polled.
"The city won't do a survey because they know we're right, that the majority of family members would say no," said Norman Siegel, a civil rights lawyer who is representing family members opposed to the city's plans.
Phil Walzak, a spokesman for Mayor Bill de Blasio, said de Blasio's administration "has engaged the community of 9/11 families continuously since entering office four months ago. This includes talking with and listening to families who have questions about this plan as well as many families who are supportive and comfortable with this plan."
The remains transfer plan was put into motion in a memorandum of understanding completed on Dec. 31, the final day of former Mayor Michael Bloomberg's administration. The memorandum, a copy of which was obtained by The Associated Press, detailed the process by which the families would be told and called for the transfer to be done without public notification.
The de Blasio administration decided to change plans and announce the transfer publicly.
Forty-one percent of the 2,753 people reported missing at the World Trade Center have not been identified.