The police said that a 4-year-old girl, Hayley Ng of Chinatown, died at the scene and that Diego Martinez, a 3-year-old boy from Chelsea, died at New York Downtown Hospital. Another 4-year-old girl was seriously injured and taken to the hospital, where she was listed in critical condition late Thursday; her name was not released. About 10 other people, children and some adults, had minor injuries, the authorities said.

The driver of the van, identified as Chao Fu, 52, of Brooklyn, was not charged; his license and registration papers were in order and he tested negative for alcohol, said Paul J. Browne, the police spokesman. Mr. Chao had double-parked and entered a store, leaving the van running and in reverse gear, thinking it was in park, Mr. Browne said.

Mr. Chao first realized that the vehicle had moved “when he came out of the store and it had already crashed,” Mr. Browne said.

The silver-colored van, a 2000 Ford, was emblazoned with the name of a downtown restaurant, China Chalet. A woman who answered the phone at the restaurant on Thursday afternoon said in Chinese that “something happened.” The woman said the company’s owner was not available for comment, and then hung up.

Image A child being carried from the scene. Fourteen preschool children from a child care center on Market Street had just left a library branch on East Broadway. Credit... Justin Lane/European Pressphoto Agency

The children had just spent an hour at the Chatham Square branch of the New York Public Library at 33 East Broadway, in the same block where the accident occurred. They had listened to a librarian read the children’s books “Snow,” about animals in a winter wonderland, and “Shark in the Park,” about a boy who spots a shark through a telescope. They also browsed in the children’s section, a library spokesman said.