Nearly 2,700 New York City students were wrongly told in recent weeks they were not eligible for seats in public school gifted and talented programs because of errors in scoring the tests used for admission, the Education Department said on Friday.

The company that both created and scored the tests, Pearson, has apologized for the mistakes, according to the department, which is now scurrying to notify parents that pupils originally locked out of the coveted programs are instead able to apply for seats.

Updated scores will be distributed within 10 days and the deadline for applying to gifted programs, originally Friday, will be extended to May 10, the department said. Only six students were incorrectly deemed qualified for the gifted programs, but they will not lose their eligibility, the department said.

All told, 4,735 students — or 13 percent of all those in kindergarten through third grade who sat for the tests — were affected by the errors, said Erin Hughes, a spokeswoman for the Education Department. Of those, 2,698 are newly eligible for seats in districtwide gifted programs, meaning they scored at or above the 90th percentile.