Trevor Phillips said he was concerned by signs of increasing segregation in schools and that the commission would launch an investigation later this year into how children from different races mixed in playgrounds.
He said schools needed to become "engines for integration" in the wake of inter-racial fighting in Birmingham in October, and in previous years in Wrexham and Oldham.
Pupils have also been attacked in a handful of race-related incidents, including two black students, aged 15 and 14, who were stabbed on a bus in Leicester on Saturday.
Mr Phillips told the National College for School Leadership's annual conference in Birmingham this week: "The role of schools in urban communities is a life or death matter.
"Schools have a vital role to play in these turbulent times and they must be part of the answer in saving our society from disintegration."
Mr Phillips warned in an earlier speech in September that Britain was in danger of "sleepwalking towards segregation".
He told teachers this week he had become more pessimistic. "We were wrong,"
he said. "Things are even worse than we thought at the time."
Examples he gave of segregation in education included the racial balance of the seven secondary schools in central Birmingham. In three, the vast majority were Asian, in three, the vast majority were white, and in only one - a Catholic school - was there a balance.
"The truth is many schools are great, but all too many are failing to prepare children for an increasingly diverse society, and if they are thinking about it, it is at the bottom of their in-tray," he said.
But Mr Phillips said that racism among teachers was no longer the problem it had been when he had grown up in London in the 1950s.