The gunman committed suicide as emergency services closed in on him. He had hundreds of rounds of ammunition left despite the fact he had already used a similar amount during his killing spree.
He also left a shotgun in his mother's car, which he parked outside the school, suggesting he intended to return for it, police said.
Lanza blasted his way into the building and used a high-power rifle to kill 20 children and six adults, including the principal who tried to stop him, authorities said.
Federal agents have been questioning staff at gun stores and shooting ranges in the state, chasing leads they hope will cast light on Lanza's life.
They are keen find out why his mother kept a cache of high-power weapons in the house and what experience he had with the guns. They also want to find a motive for his decision to kill young children.
Connecticut Governor Dannel Malloy said Lanza shot himself as police entered the building.
"We surmise that it was during the second classroom episode that he heard responders coming and apparently at that, decided to take his own life," Mr Malloy said.
Lanza shot his mother, Nancy Lanza, to death at their home, drove to Sandy Hook in her car with at least three of her guns, forced his way in and opened fire, authorities said.
Nancy, 52, is said to have been a "big, big gun fan" who taught her son how to shoot.
Dan Holmes, the owner of a local landscaping firm, said Mrs Lanza once showed him a high- specification rifle she had bought, adding: "She was very proud of it."