Mayor Bill de Blasio said Friday he’s considering abolishing tests for 4-year-olds to get into the city’s gifted and talented program — then was criticized for the position by a caller who said she’d leave the city if the exams were cut.

“That could be part of the process, I think it’s a great question,” the mayor answered WNYC radio host Brian Lehrer when asked about eliminating those tests.

“If we think of isolating a small group of kids and calling them gifted and talented and then leaving a whole bunch of other kids without the opportunity to display their gifts and have them supported, something’s wrong there,” the mayor said.

Until Friday, de Blasio had been reluctant to give an opinion about a controversial recommendation by a diversity panel to scrap the gifted and talented program systemwide.

De Blasio said he’s going to take a year before making any changes.

The mayor convened the School Diversity Advisory Group in 2017 to “reshape citywide policies and practices such as admissions and program planning.”

Panel members want the Education Department to replace gifted schools with an unspecified system that expands ­“enrichment.”

That is not sitting well with Brooklyn Councilman Robert E. Cornegy Jr., who is on the education committee. He said he doesn’t trust the DOE to overhaul the Gifted & Talented program.

“What the School Diversity Advisory Group is proposing offers a pretty utopian view of the Department of Education,” Cornegy said.

“In the DOE’s current iteration, Gifted & Talented has provided the best tool for success for high- performing students in the city,” he said.

“It is hard for me to consider other proposals from the group when we have a broken system. It’s a vote of no confidence from me on implementing this in any time frame that a parent could be satisfied with,” Cornegy said.

A few minutes later, Lianne, an Upper West Side mother of two public school kids, called in to the radio show to blast the mayor for his position.

“If my son had not tested well I would be living in New Jersey,” the caller said, adding that she’s worried about her second child’s education.

“I feel like your’re educating kids in pre-K then dropping them at K” she said.

“You feel that, but I disagree with that,” the mayor answered.

“I’m one of those middle-class families that’s on the fence about moving out of New York because I have a son that I’m now applying to middle school and I have no faith that he’ll get into a good school,” Lianne said. “Do you want to lose families like me?”

De Blasio conceded that city middle schools need “to be stronger” and pledged to connect the caller with a Department of Education official to help her navigate the admissions process.