NEWTOWN, Conn. — A man killed his mother at their home and then opened fire Friday inside the elementary school where she taught, massacring 26 people, including 20 children, as youngsters cowered in fear to the sound of gunshots reverberating through the building and screams echoing over the intercom.

The 20-year-old killer, carrying at least two handguns, committed suicide at the school, bringing the death toll to 28, authorities said.

The rampage, coming less than two weeks before Christmas, was the nation’s second-deadliest school shooting, exceeded only by the Virginia Tech massacre that claimed 33 lives in 2007.

“Our hearts are broken today,” a tearful President Barack Obama, struggling to maintain his composure, said at the White House. He called for “meaningful action” to prevent such shootings. “As a country, we have been through this too many times,” he said.

Police shed no light on the motive for the attack. The gunman, Adam Lanza, was believed to suffer from a personality disorder and lived with his mother, said a law enforcement official who was briefed on the investigation but was not authorized to discuss it.

Panicked parents looking for their children raced to Sandy Hook Elementary in Newtown, a prosperous New England community of about 27,000 people 60 miles northeast of New York City. Police told youngsters at the kindergarten-through-fourth-grade school to close their eyes as they were led from the building so that they wouldn’t see the blood and broken glass.

Schoolchildren — some crying, others looking frightened — were escorted through a parking lot in a line, hands on each other’s shoulders.

Law enforcement officials speaking on condition of anonymity said that Lanza killed his mother, Nancy Lanza, then drove to the school in her car with at least three guns, including a high-powered rifle that he apparently left in the back of the vehicle, and shot up two classrooms. Nancy Lanza was a part-time substitute at the school, according to a parent.

Authorities gave no details on exactly how the attack unfolded. But a custodian ran through the halls, warning of a gunman on the loose, and someone switched on the intercom, alerting people in the building to the attack — and perhaps saving many lives — by letting them hear the hysteria going on in the school office, a teacher said.

Teachers locked their doors and ordered children to huddle in a corner or hide in closets as shots echoed through the building.

State police Lt. Paul Vance said 28 people in all were killed, including the gunman, and a woman who worked at the school was wounded.

Lanza’s older brother, 24-year-old Ryan, of Hoboken, N.J., was being questioned, but a law enforcement official said he was not believed to have had a role in the rampage. Investigators were searching his computers and phone records, but he told law enforcement he had not been in touch with his brother since about 2010.

The officials spoke on the condition of anonymity because they were not authorized to discuss the unfolding investigation.

At one point, a law enforcement official mistakenly identified the gunman as Ryan Lanza. Brett Wilshe, a friend of Ryan Lanza’s, said Lanza told him the gunman may have had his identification. Updates posted on Ryan Lanza’s Facebook page Friday afternoon read, “It wasn’t me” and “I was at work.”

Robert Licata said his 6-year-old son was in class when the gunman burst in and shot the teacher. “That’s when my son grabbed a bunch of his friends and ran out the door,” he said. “He was very brave. He waited for his friends.”

He said the shooter didn’t utter a word.

Stephen Delgiadice said his 8-year-old daughter heard two big bangs. Teachers told her to get in a corner, he said. “It’s alarming, especially in Newtown, Connecticut, which we always thought was the safest place in America,” he said. His daughter was uninjured.

Theodore Varga was in a meeting with other fourth-grade teachers when he heard the gunfire. He said someone had turned on the intercom so that “you could hear people in the office. You could hear the hysteria that was going on. I think whoever did that saved a lot of people. Everyone in the school was listening to the terror that was transpiring.”

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