A foggy morning procession began shortly before 7 a.m. at the Office of the Chief Medical Examiner on Manhattan's East Side. The three vehicles transporting the remains were accompanied by police and fire department vehicles.
The remains will be transferred to a repository 70 feet underground in the same building as the National September 11 Memorial Museum.
The medical examiner will oversee the facility, and it will be open for family visits. Officials hope that improvements in technology will eventually lead to the identification of the 7,930 fragmentary remains.
The death toll stemming from the attacks at the World Trade Center stands at 2,753. Of those, 1,115, or 41 percent, have not been identified.
Not everyone was pleased with the decision to keep the remains underground, though the plan has been in the works for years.
Wearing black bands over their mouths, a group of victims' family members protested during the procession. They want the remains stored above ground in a monument, separate from the museum.
"It's horrible. I am so angry. I am so angry. I am outraged," said Sally Regenhard, whose firefighter son was killed at the trade center.
For many, storing the remains above ground is a display of respect.
"The human remains of my son and all of the 3,000 victims should be in a beautiful and respectful memorial, not in the basement of a museum," she said.
Rosemary Cain, who also lost her firefighter son at the trade center, was also upset about the transfer.
"I don't know how much of him is down here; if it's one little inch, I want it treated respectfully," she said. "I want it above ground. I don't want it to be part of a museum. I don't want it to be part of a freak show."
Other family members, like Lisa Vujak, do support the plans. Vukaj lost her 26-year-old brother. She said the new home for the remains is "a fitting place until technology advances" and new techniques are available to identify their loved ones.
The Associated Press contributed to this report.