The group of 28 town elected officials voted unanimously in favor of a plan that would construct a new building in the same location.
The proposal now goes to the local school board, which has final authority.
The panel had narrowed a list of choices to renovating or rebuilding on the school site or building a new school on property down the street. Each would cost between about $48 million and $60 million.
The 430 surviving students are attending a renovated school renamed Sandy Hook Elementary School in the neighboring town of Monroe.
Officials had said that whatever choice is made, a new or renovated school wouldn't be ready by Aug. 27, the start of the next school year.
A study found building a new school on the existing site would cost $57 million.
Sandy Hook Elementary School hasn't housed students since the killings. Some town residents said the school should be torn down because they couldn't imagine sending children back there. Others favored renovating the school, with some saying that tearing it down would be a victory for evil.
Residents of towns where other mass school shootings occurred have grappled with the same dilemma. Some have renovated, some have demolished.
Columbine High School in Colorado, where two student gunmen killed 12 schoolmates and a teacher in 1999, reopened several months afterward. Crews removed the library, where most of the victims died, and replaced it with an atrium.
Virginia Tech converted a classroom building where a student gunman killed 30 people in 2007 into a peace studies and violence prevention center. And an Amish community in Pennsylvania tore down the West Nickel Mines Amish School and built a new school a few hundred yards away after a gunman killed five girls there in 2006.
On the morning of Dec. 14, gunman Adam Lanza, who had killed his mother at their Newtown home, went to Sandy Hook Elementary School and opened fire with an assault rifle, killing the 20 children and the six adults. He killed himself as police arrived at the school.
The school shooting, one of the deadliest in U.S. history, has spurred national debate about gun control and Second Amendment rights.
Police have not disclosed possible motives for the Newtown killings. Law enforcement officials have said Lanza showed an interest in other mass killings and played violent video games.
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