A crazed gunman dressed in black went on a rampage at a Connecticut elementary school this morning, in a massacre that left the shooter and 26 others dead — including 20 children — and the number of fatalities could rise.

Adam Lanza, 20, shot his mother Nancy Lanza dead at their family home before driving to the school and targeting a kindergarten class at Sandy Hook Elementary School in Newtown, Conn., sources said. Sources also told The Post that Lanza “had a dispute” with his mother.

Lanza was found dead inside the school from a self-inflicted gunshot wound, an official told the AP.

Principal Dawn Hochsprung is among those killed. CBS 2 is reporting that teacher Natalie Hammond, 40, is in surgery and is expected to survive.

“She was wonderful. The students had someone to go to if they needed someone, she was always there for them,” said Dianne Shay, herself a substitute teacher and Hochsprung’s neighbor. ” She was very genuine, very upbeat and outgoing.”

Shay said Hochsprung had two adult daughters.

Lanza used two handguns — a Glock and a Sig Sauer — and a .223-caliber assault rifle, an official said. An official also said Lanza’s girlfriend and another friend are missing in New Jersey.

Police in Hoboken questioned Lanza’s older brother, Ryan, 24, but an official told the AP he is not believed to have had any involvement in rampage.

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The shooter was found with an ID that bore his brother’s name, a law-enforcement source said, but there is no indication that it was stolen. A source told The Post Ryan has told investigators he last saw Adam in 2010 and that Adam is autistic.

Ryan Lanza has a Facebook page that posted updates Friday afternoon that read that “it wasn’t me” and “I was at work.”

At least one parent said Lanza’s mother was a substitute teacher at the school. But her name did not appear on a staff list. And the law enforcement official said investigators were unable to establish any connection so far between her and the school.

The tragedy is among the nation’s deadliest school shootings, exceeded only by the Virginia Tech massacre in 2007, which left 32 people and the gunman dead.

Heartwrenching dispatch calls reveal that Lanza’s rampage took only minutes.

The first word of the horrifying Newtown school shooting went out over the town’s police radio at 9:36 this morning.

At 9:46 a.m., as police searched the school, someone who could not hide the emotion in his voice radioed these haunting words: “I’ve got bodies here. Need ambulances.”

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.

“We were in my art teacher’s room. We heard some gunshots – like 20. Then the police came with guns and told us to close our eyes,” said fourth-grader Venesa Bajraliu, 9.

“I heard gunshots and I saw policemen. My teacher was scared and a little shaky. We went into the office and police came and took us into the firehouse.”

She heard screams and gunshots over the intercom of the school, said her brother, Nergim, 17.

Nergim and his mother were the first to arrive at the school. He saw three young victims, who appeared wounded.

“When I saw the girl come out with police, the girl was splattered with blood.”

An emotional President Obama addressed the nation this afternoon.

“Our hearts are broken today for the parents, grandparents, sisters and brothers of these little children and for the families of the adults who were lost,” a teary-eyed Obama said.

Obama also expressed his grief for the parents of survivors, who in a scene of mass chaos, rushed to a nearby firehouse to pick up their children.

“Our hearts are broken for the parents of the survivors as well, for as blessed as they are to have their children at home tonight, they know that their children’s innocence has been torn away from them too early. There are no words that will ease their pain.”

Mom Carrie Battaglia told The Post that the firehouse where she was told to pick up her children was in a state of chaos.

“It’s a mob scene,” said Battaglia, 39, whose daughters, 6 and 8, attend the school. She said teachers were handing out water and crackers.

“We’re just thankful our kids our OK, ” Battaglia said between tears. “I wouldn’t think anything like this would ever happen.”

Her husband, David Battaglia, said, “It’s intense — people are trying to find their children.”

Jennifer Belward said her three- and four-year-old children were at the Children’s Adventure Center preschool next door to the elementary school.

“They put them on lockdown and they were sitting in their cubbies eating pizza and watching a movie,” she said, as she walked hand-in-hand with them up Riverside Road.

She said her children were unaware of what happened.

Joanne Didonato, the principal’s secretary, said she called in sick today – something she rarely does.

“Of all days,” she said. “I want to go be with my colleagues. I’m sick over the news. I’ve been on the phone with some people but they don’t know. Everything is just up in the air right now, I know nothing.”

“They’re saying children are killed. I just can’t handle that. We have great kids in our school and I’m just so upset over that.”

According to a witness report, the school’s principal and another staffer were killed while another staffer was shot in the leg after a gunman opened fire in a hallway.

A witness said gunshots were heard in the hallway during a meeting and that “100 rounds” must have been fired, according to CNN. After the shots were fired, three people ran into the hallway but only the vice principal crawled back.

Cops responded to reports of the shooting at Sandy Hook Elementary just after 9:40 a.m., and said the gunman was in the school’s main office, according to reports.

The newspaper reports that as of 11 a.m., police were still searching the school with dogs.

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Parents told the Hartford Courant that some students were still in the school at 10:30 a.m. Groups of students, some crying and holding hands, were seen were being escorted away from the school by their teachers.

One child leaving the facility told the newspaper that there was shattered glass everywhere. A police officer ran into the classroom and told them to run outside and keep going until the reach the firehouse, according to the report.

Three people from the scene were taken to Danbury Hospital, a hospital spokeswoman told NBC. The hospital is on lockdown.

“There are no visitors allowed today. This hospital is on lockdown. Nobody is getting in or out,” one officer told The Post.

“We grieve for all the people in our community afffected by today’s tragedy. We offer our heartfelt sympathy and prayers to all involved,” said Dr John Murphy president and CEO of Western Connecticut Health Network.

“This is our home, this is where we live. We are here, we are open and no longer on lock down as we were earlier in the day. We are fully operational to provide any and all care and support for the people who need us today as well as those who will need us in the days to come.”

Murphy said that the shooting was the most traumatic event he has “ever experienced or considered. It’s unthinkable and we’re all hurting here.”

Earlier, Danbury Hospital posted a statement to their Facebook page: “We are here to care for any victims and their families in any way they need us. Our hearts and prayers are extended to anyone involved in this terrible tragedy. To date, three patients have been transported to Danbury Hospital from the scene. Out of abundance of caution and not because of any direct threat Danbury Hospital is under lockdown. This allows us simply to focus on the important work at hand. We will keep you apprised of any additional information as details are confirmed.”

The seven schools in the district were in lockdown mode, said Kathy June, of the Newtown Public School District.

Stephen Delgiadice said his 8-year-old daughter heard two big bangs and teachers told her to get in a corner. His daughter was fine.

“It’s alarming, especially in Newtown, Connecticut, which we always thought was the safest place in America,” he said.

Brenda Lebinski, whose 8-year-old daughter attends the school, was among the parents who raced to check on their children.

“I saw her and it was the happiest moment of my life,” she said.

Connecticut’s governor was on the scene in Newtown.

Ambulances surrounded the school, about 60 miles northeast of of New York, and parents were running toward the building as a helicopter flew overhead.

State police said Newtown police called them around 9:40 a.m. A SWAT team was among the throngs of police to respond.

A photo posted by The Newtown Bee newspaper showed a group of young students — some crying, others looking visibly frightened — being escorted by adults through a parking lot in a line, hands on each other’s shoulders.

Community members later gathered at a Newtown church, holding a vigil for the victims.

People lit candles and held hands and sang, reflecting on the tragedy, numbed by the awful, twisted violence.

Additional reporting by Frank Rosario, Melanie Gray and Erin Calabrese. With AP