New York (CNN) -- A group of 9/11 victims' family members are up in arms over a plan to house the unidentified remains of those who died at ground zero in the lower level of the museum being built to honor the tragedy.
Critics are against storing the remains underground and claim they were never consulted about the decision of where to build a repository. The plan calls for a repository and laboratory controlled by the city medical examiner to be built on the ground floor of the National September 11 Memorial and Museum, which is set to open next fall.
"Many individual family members were open to the idea of someday returning the remains to ground zero at a proper and respectful, above-ground memorial and repository," said Sally Regenhard, who lost her son on 9/11.
Regenhard spoke at a news conference held at the site of the World Trade Center on Sunday.
"These souls will never rest in peace when they're buried 70 feet underground," said Rosemary Cain, whose son died on September 11.
Protesters called on project officials to reach out to all 2,789 victims' families for approval before building the repository inside the museum.
Alice Greenwald, director of the museum, said the plan to build a repository in the same building as the museum has been public since 2006 and that victims' families have been involved the entire time. The remains, which are currently at a temporary location near the Office of the Chief Medical Examiner's on 30th Street, will be moved to ground zero in 2013.
"We're trying so hard to be responsive to families," Greenwald said. "I understand the pain that they are in and I'm deeply sensitive to what they have been through. But I think they are characterizing what we're doing in a way that is not true."
Although visitors to the museum will use the same entrance as family members who are paying their respects to the repository, the two are separate entities, Greenwald said.
The repository and the private room for 9/11 victims' family members are being built, funded and run by the Office of the Chief Medical Examiner of the City of New York, she added. There, the agency will continue to make DNA identifications of the remains.
The repository and private family room will be separated from the museum by a wall engraved with a quote from Virgil's Aeneid -- "No day shall erase you from the memory of time."
Greenwald said museum staff will be on hand during business hours and when the museum is closed to escort visiting family members to the private viewing area.
Still, many family members said they were not involved in the decision to keep the unidentified remains within the museum.
"Family members should make the final decision regarding the human remains of their loved ones," Regenhard said.
Not all 9/11 victims' family members share this opinion, though.
Charles G. Wolf, who lost his wife on September 11, said he is upset by the protests against the current repository plan.
"The museum is being very sensitively designed," he said. "It is respectful."