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The remains were found in rubble excavated from a manhole near the site of the World Trade Center. Relatives say the find proves the need for a thorough new search of the area around Ground Zero.
"We can no longer rely on accidental discoveries," said WTC Families for Proper Burial in a statement.
"This must be a deliberate search. May this awful news be the catalyst needed to go back and do the job well."
Families of more than 1,100 of the victims of 9/11 have never received any remains of their loved ones.
The campaign group is to hold a news conference over the latest discovery later on Friday.
Recent discoveries have sparked angry calls for construction to be halted, and answers as to why the first search was not exhaustive.
The city has responded by promising to hire 10 forensic anthropologists to help find and identify additional remains, but some victims' families say this is not enough.
"We demand a scientific, well-organised controlled survey of Ground Zero by a reputable entity," a statement by organisers of Thursday's rally said.
"We must show our absolute solidarity at the site where the remains of the 9/11 dead have lain ignored and unburied for over five years.
"It is time to stand up and be counted. There can be no more haphazard discovery of human body parts and personal effects."
New York Michael Bloomberg has said that the city should be proud of the original search, in which almost all areas were gone through.