The city's Education Department said Friday the company that created and scored the admission tests has apologized and department officials were notifying parents that students originally blocked from the talented and gifted programs can apply, The New York Times reported.
Updated scores will be distributed within 10 days and the original application deadline, which was Friday, will be extended to May 10, the department said.
Six students incorrectly scored as qualified for the programs won't lose their eligibility, the department said.
Thirteen percent of the students in kindergarten through third grade who took the tests -- 4,735 students -- were affected, Education Department spokeswoman Erin Hughes said.
Of that total, 2,698 students were newly declared eligible for district-wide programs, scoring at or above the 90th percentile.
Chancellor Dennis Walcott said the errors made by the testing company, Pearson, were "unacceptable."
"Pearson has an established record in this field and we depend on its professionalism and deep capacity to deliver for the public," Walcott said in a statement. "But in this case, they let our children and families down. I have told the company's officials in no uncertain terms that I expect this will never happen again."