An investigation found that the driver had double-parked and jumped out of the van to make a delivery, thinking he had left it running in park, police said. Instead, the van traveled backward and hopped a curb on the opposite side of the street.
Though the driver initially was held for questioning, "It turns out this was an accident," police spokesman Paul Browne said.
An examination of the van and a security video tape supported the driver's account, Browne added.
Many were pre-school students, walking and holding hands in "daisy chain" formation while accompanied by adult supervisors.
A 4-year-old girl, identified as Hayley Ng, was pronounced dead at the scene. Three-year-old Diego Martinez later died at New York Downtown Hospital.
"There was an extraordinary effort," Chief Medical Officer Dr. Warren Licht said. "Our emergency room team, consisting of physicians, nurses, EMS workers, all tried heroically to do the best they could to save this child's life."
A third child is listed in critical condition at Bellevue Medical Center.
As many as 14 others, children and adults, were treated for various minor injuries.
The children were walking from a library visit back to the Red Apple Child Development Center at 25 Market Street.
Police closed a block of East Broadway for the investigation. The grey van, with the name of catering company China Catering, was at rest on the sidewalk.
Chinese interpreters were requested to the scene for the victims.
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