New York (CNN) -- Relatives of firefighters and others killed in the 9/11 attacks are urging New York state officials to step in and postpone the medical examiner's plans to sift through untouched debris for human remains.
The group is calling for an outside investigation of the New York City Office of the Chief Medical Examiner and its handling of DNA cases from previous resifting projects.
"A long-standing culture of mistakes, mishaps and lack of oversight" has jeopardized not only criminal cases, but also 9/11 human remains cases from the World Trade Center site, the group said in a statement.
The relatives of the victims want to halt all resifting until an investigation is complete.
"How can we be certain that the same practices that allowed over 50 DNA samples to be mishandled as well as DNA evidence in 26 rape cases to go undetected (at the medical examiner's office) will not likewise taint the DNA investigation process of our heroes and loved ones of 9/11 as well," the statement says.
New York City will begin sifting through 590 cubic yards of material from the site on Monday, the city said.
The city expanded its search for human remains at the World Trade Center site in October 2006, when potential human remains were found in a manhole there, the city said in a news release. Since then, the city has identified 34 new victims of the 9/11 attacks and linked more than 2,435 human remains to previously identified victims.
Of the 2,753 men and women killed in the attacks, only 1,634 have been identified. Of the remains recovered from the site, 62% have been matched to a victim.
The material to be sifted includes 539 cubic yards gathered from an area known as the Vehicle Security Center at the World Trade Center site, which had previously been inaccessible. Material was also gathered from the World Financial Center and the West Side.
The city will use a new sifting procedure developed since 2006 at a forensic mobile sifting platform at Fresh Kills in Staten Island.