Human remains - some reportedly as large as arm or leg bones - have been found at the site of the 11 September 2001 attacks in New York.
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.
'Never fully searched'
"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.
The BBC's Jeremy Cooke in New York says that for some of the relatives, the find is an indication that the site has never been fully searched for the remains of the 2,749 people who died there.
Charles Wolfe, whose wife Kathryn was among the victims, told the BBC he was totally shocked by the new discovery of body parts, adding that in his view, there was a major shortfall in the original recovery effort.
The material excavated from the manholes was removed from the site without anyone noticing it contained the remains, said utility company Consolidated Edison.
On Thursday, the Port Authority contractor spotted the remains, the Associated Press news agency said.
Some of the remains were as big as arm or leg bones, Steve Coleman, a spokesman for the Port Authority, was quoted by AP as saying.
Construction workers have been instructed to look for human remains and notify the medical examiner's office when they find them.
"No official identifications have been made at this time and the New York City Police Department and the Office of the Chief Medical Examiner are heading up the investigation," said Patrick J Brennan of the Mayor's Community Assistance Unit was quoted by the AP news agency.
The discovery comes just weeks after the fifth anniversary of the attacks.
Earlier this year, construction workers in New York discovered 74 bone fragments from 9/11 victims. The remains were found mixed in with roofing material at the condemned Deutsche Bank building, which stands next to Ground Zero.