The dead included the principal, Dawn Hochsprung (47). The 'New York Times' last night said that Lanza had walked into his mother's classroom, shot and killed her and killed the 20 pupils inside.
Two young girls described seeing the gunman go into their classroom and shoot their teacher. One entire classroom of children was reportedly unaccounted for.
The White House said US President Barack Obama was being kept informed and had "enormous sympathy" for the families.
Spokesman Jay Carney said there would be a day for discussion of gun control "but I don't think today is that day".
The gunman, reportedly wearing body armour and a mask, was discovered dead in a classroom, but it was not clear whether he took his own life or was shot by police.
A second man wearing camouflage trousers was seen being handcuffed and one witness described him shouting: "I didn't do it."
One witness, a mother who was in a meeting with the principal and half-a-dozen other people at about 9.40am, described hearing a "pop pop pop" in the hallway.
She said that the principal, vice principal and school psychologist went out into the corridor.
"Three people went out into the hallway and only one person came back. The vice principal was shot in the leg or the foot and came crawling back."
The witness described cowering under a table and said that at least 100 rounds might have been fired. Two bodies were seen lying in the hallway in a pool of blood.
Brenda Lebinski, another parent, said that her eight-year-old daughter and other children were saved by a teacher who locked them in a closet.
"My daughter's teacher is a hero, she locked all the children in a closet and that saved their lives," she said.
"It was horrendous. Everyone was in hysterics – parents, students. There were kids coming out of the school bloodied. I don't know if they were shot, but they were bloodied."
One nine-year-old boy said: "I was in the gym. We heard lots of bangs and we thought it was the custodian knocking stuff down. Then we heard screaming.
"Then police came in and said, 'Is he in here?'. Then they ran out and we went to the closet in the gym and hid. Then we ran to the fire house and saw a guy on the floor in handcuffs. We were just happy to be alive."
Soon after the shootings police raided a home in the neighbouring state of New Jersey. One person was said to have been found dead at the scene.
Earlier this year, in a letter addressed to "Members of our Sandy Hook family", the principal outlined details of a new security policy at the school.
She said that exterior doors would be locked during the day and all parents would be required to ring the doorbell and visually checked by staff before being let in.
Lisa Procaccini, whose eight-year-old daughter survived by hiding in a bathroom, said: "Why is this happening so much? How are we going to stop this?"
It was the latest in a series of mass shootings over the past several years.
In 2007 Seung-Hui Cho shot and killed 32 people and wounded 17 at Virginia Tech university. In July this year James Holmes killed 12 and injured 58 at a cinema in Aurora, Colorado. (© Daily Telegraph London).