Officials admitted the policy could mean one in five of the city's third-grade pupils having to repeat the year from September. The city's mayor, Michael Bloomberg, told New Yorkers in his annual address on January 9 that students must earn the right to progress, and he was starting with eight-year-olds to catch youngsters at a pivotal age.
"Third grade is critical. By fourth grade students are supposed to move from learning to read to reading to learn. If they can't read, they can't do it."
Klein announced a $25 million (pound;16m) package of measures for remedial students, including optional summer lessons and the chance to re-sit the exam, extra-curricular coaching and tailored teaching.
So-called grade retention has the unusual distinction of being an education policy that President George Bush and his predecessor in the White House, Bill Clinton, would agree on. Ending social promotion was a pet policy of Clinton's, and touting his education reforms earlier this month, President Bush called for an end to "this business of just shuffling kids through the schools".
New York joins a growing list of US education authorities tying student promotion to test scores, including new state-wide laws in Texas and Florida.
"Social promotion is a cancer that eats at the heart of public education," said Philadelphia schools chief, Paul Vallas, who previously masterminded America's longest-standing and largest grade-retention scheme in Chicago.
"Promoting children who aren't capable of working at grade level is a disservice to them and others," said Vallas. "Teachers begin to dumb down lessons, and students who can do the work are disadvantaged."
But experts say grade retention discourages weaker students, making them likelier to drop out.
Jere Brophy, Michigan state university education professor, said retained students have drop-out rates three to four times higher than those not kept back.