The mayor, struggling to close a $400 million budget gap, blamed a huge cut in state aid, The New York Times reported. He said aid has dropped from 45 percent of the total city education budget in 2008 to 39 percent in the coming fiscal year.
About 1,500 of the job cuts would come through attrition and the rest from layoffs.
"I understand the frustration that parents and teachers feel; I feel it too," he said as he presented his final budget. "We are not going to walk away from our education system."
Bloomberg's budget now goes to the City Council for approval. Speaker Christine Quinn said she plans to do what she can to reduce or eliminate the cuts.
"We continue to ask the least among us to bear the brunt. I'm really concerned," Councilwoman Melissa Mark-Viverito said.
About 75,000 teachers work in the New York City public schools.