A law enforcement official said the 20-year-old gunman took his own life after he inflicted the horrible carnage at Sandy Hook Elementary School, The New York Times reported.
"Evil visited this community today," Connecticut Gov. Dannel Malloy said. "We are all in this together."
Another adult was wounded in the shooting spree at the school. Police found the body of his mother, Nancy Lanza, shot dead at the residence in town that they were believed to have shared.
Residents of the shattered community of about 27,500 people and the surrounding region gathered for a vigil Friday night to pray and support the grieving families, the Hartford (Conn.) Courant reported.
Stephen Gray of Hartford said he had watched the day's events unfold on television.
"It just got worse and worse," Gray said. "I just had to be with other people and hopefully feel a little better."
Jane Carroll of Hartford said the shootings were "just so sad, so very sad."
"We're just sending prayer. There's nothing else we can do -- just prayer," she said.
"I'm just pretty heartbroken," said Amanda Pepin, who attended with her 9-year-old daughter, Gia Stanco. "I can't imagine that happening to my child."
"We might not be able to make sense of this today or tomorrow, but it's not impossible for us to come together to show our children that we love them," Hartford Mayor Pedro Segarra said.
Lanza, described variously as dressed in black or combat gear, used two handguns, a Sig Sauer and a Glock, the Times said. Police also found a Bushmaster .223 M4 carbine rifle at the scene that they believed he had brought along, the newspaper said.
MSNBC reported officials had initially misidentified the shooter to NBC News as Lanza's 24-year-old brother, Ryan. But a senior official later said Ryan Lanza was cooperating with authorities and was not believed to have been involved. He told police his brother had a history of mental illness, the network said.
A motive, however, had not been determined, the Courant said.
Two law enforcement officials said the guns used in the massacre were purchased legally and were registered to the gunman's mother, MSNBC said.
State Police Lt. Paul Vance told reporters the gunman shot up two classrooms in one section of the school, which serves children in kindergarten through fourth grade.
"We heard, like, lots of bangs," 9-year-old Brendan Murray told CNN.
School therapist Diane Day said she was sitting with the principal, other staff members and a parent when the shooting started, The Wall Street Journal reported.
"We were there for about 5 minutes chatting and we heard, 'pop pop pop,'" she said. "I went under the table.'
Day said Principal Dawn Hochsprung, who was reported to have been among those shot, and a school psychologist immediately ran out of the room.
"They didn't think twice about confronting or seeing what was going on," she said.
"At first we heard a bunch of kids scream, and then it was just quiet and all you could hear was the shooting."
The school's lead teacher was shot through the door as she pressed her body against it to hold it shut, Day said.
"She was our hero," Day said.
Vance said 18 children were dead at the school and two others were pronounced dead at Danbury Hospital. The bodies of six adults and the gunman also were found in the school.
Police escorted a second man out of nearby woods and took him into custody.
"I saw some of the bullets going past the hall ... then the teacher pulled me into her classroom. ... It sounded like someone was kicking the door," one child told reporters.
"I saw policemen -- lots of policemen in the hallway with guns," 9-year-old fourth grader Vanessa Bajraliu told the Courant. "The police took us out of the school. We were told to hold each others' hands and to close our eyes. We opened our eyes when we were outside."
The president, who ordered the nation's flags lowered to half-staff, went through a litany of such incidents.
"We're going to have to come together and take meaningful action to prevent more tragedies like this, regardless of the politics," Obama said.
"We've endured too many of these tragedies in the past few years. And each time I learn the news I react not as a president but as anybody else would -- as a parent. And that was especially true today. I know there's not a parent in America who doesn't feel the same overwhelming grief that I do.
"The majority of those who died today were children -- beautiful little kids between the ages of 5 and 10 years old. They had their entire lives ahead of them -- birthdays, graduations, weddings, kids of their own. Among the fallen were also teachers -- men and women who devoted their lives to helping our children fulfill their dreams.
"Nothing can fill the space of a lost child or loved one."
Vance said police were summoned to the school in the scenic community about 65 miles northeast of New York City shortly after 9:30 a.m. and began an "active shooter search" of the building.
Police "did search every nook and cranny and every portion of the school," Vance said.
Newtown Police Lt. George Sinko said the shooting was "the worst thing we've experienced in town." He said crisis intervention counselors were available to the community.
"We just have to think about the families right now and do what we can for them," Sinko said.
WNBC-TV, New York, reported the gunman went to the school after first killing his father. Vance said search warrants had been executed for the shooter's home.
Malloy issued his condolences after meeting with parents.
"You can never be prepared for this kind of incident," he said, adding that it leaves a "mark on the community and every family impacted. ... These were beautiful children who had their lives taken away from them."
A first-grade teacher hid in the bathroom with her class and tried to keep them calm, ABC News reported. She said one of the children told her, "I just want Christmas. I don't want to die."
Alexis Wasik, 8, told ABC classmates were screaming and crying, and that she felt sick to her stomach. Her mother said she couldn't believe something like this could happen in Newtown.
"You drop your kids off, say, 'Have a good day,' 'I'll see you later.' You never expect anything like this. Not here," the mother said.
Officers and teachers led children, many of them crying, single file to a staging area at a firehouse where parents picked them up, the Courant reported.
"We ran down to the firehouse and there was a man pinned down with handcuffs on," a young boy told CNN.
"Who would do this? What kind of person would do this?" screamed a young man whose sister attended the school.
Another young man said his sister heard several loud booms, MSNBC reported.
The Newtown Bee reported numerous ambulance crews were on the scene, but a triage nurse told CNN they were sent away.
"We were told there was nothing for them to do," she said.
Bloomberg said Obama should send a bill to "fix this problem -- and take immediate executive action."
"Calling for 'meaningful action' is not enough," Bloomberg said. "We have heard that rhetoric before. What we have not seen is leadership -- not from the president and not from Congress. That must end today. This is a national tragedy and it demands a national response."
The Times said Friday's shooting spree was the second deadliest in U.S. history, after the 2007 massacre at Virginia Polytechnic Institute, when 32 died.