Parents taking their children to Head O'Meadow Elementary for what would have been the first day of classes since 20 students and six adults were killed Friday at Sandy Hood Elementary School were turned away by police, ABC News reported.
The schools are in the same district less than 5 miles apart.
Head O'Meadow's principal sent an email to parents informing them the school would be closed Tuesday because of threats.
"As was predicted by the police that there would be some threats, the police were prepared and have us in lockdown, which is normal procedure," the email said. "Due to the situation, students will not come to school today. Please make arrangements to keep them home."
New security systems were being installed at other Newtown schools.
ABC said law enforcement officials classified Sandy Hook Elementary School as an active crime scene that the building would remain closed. Furniture and supplies from the school were being transported to a former middle school in Monroe, Conn., about 10 miles away.
WTNH-TV, New Haven, Conn., said Sandy Hook students would begin classes in Monroe Wednesday.
More funeral services, including those of two 6-year-old children, and wakes were held Tuesday for the victims of gunman Adam Lanza, 20, who killed himself during the shooting rampage. Police said Lanza also killed his mother, Nancy Lanza, in the home they shared before he went to Sandy Hook.
Meanwhile, a former director of security for Newtown Public Schools offered more information about the gunman, CNN said.
Richard Novia said Lanza had Asperger's syndrome, a high-functioning form of autism, based on documents and conversations he had with Lanza's mother. Novia said he would have been told of students who may pose a problem to themselves or others as part of his job, which he left in 2008.
However, Novia said he never thought Lanza posed a threat nor thought he could commit such violence.
The grassroots group Newtown United said it was sending a delegation to Washington to meet with the Brady Campaign to Prevent Gun Violence and families from movie theater massacre in Aurora, Colo., that occurred in July.
The Newtown group, formed Sunday, said it wants to create meaningful dialogue about what may have led to the tragedy.
In Washington, pro-gun lawmakers said they were open to new gun laws.
Sen. Charles Grassley, R-Iowa, called for a commission to study the shootings, but said it should include mental health issues and "certainly can't be a debate just about guns."
Sen. Marco Rubio, R-Fla., called for a "comprehensive study of our laws'' aimed at preventing further shooting tragedies, possibly including measures to keep guns out of the hands of criminals and people with mental illnesses.
Pro-gun Democratic lawmakers saying they were open to new gun laws included Sen. Joe Manchin and Rep. Nick Rahall, both of West Virginia, Sen. Mark Warner of Virginia and Rep. Joe Donnelly of Indiana.
Manchin, who received an "A" rating from the National Rifle Association, told MSNBC assault rifles weren't needed for hunting.
"It's time to move beyond rhetoric" on weapons restrictions, he said.
A Washington Post-ABC News poll indicated 54 percent of adults favor stricter gun control laws in the country, while 43 percent oppose. A CBS News poll indicated 57 percent of Americans support stricter gun laws while 30 percent said they think gun laws should be kept as they are.
Texas Gov. Rick Perry said he was all right with the idea of school districts arming teachers if that was found the best way to keep schools safe, CNN reported.
If Texas residents are properly background-checked, trained and have a concealed handgun license, "you should be able to carry your handgun anywhere in the state," Perry told CNN affiliate WFAA.
National sporting goods chain Dick's Sporting Goods removed all guns from its store closest to Newtown out of respect for the victims, the company said.