The remains are stored in a large tent near the medical examiner's office on the east side of Manhattan.
Family members clutched pictures of their loved ones as they placed a wreath there on the eve of the 10th anniversary of the attacks.
They criticized the city's plan to move the remains to the museum at the redeveloped trade center site.
Sally Regenhard, whose firefighter son Christian was killed in the attacks, says human remains don't belong in a museum.
More than 1,100 victims have no identifiable remains. The medical examiner's office says it will continue DNA testing on bone fragments recovered from ground zero.