"When we get information like this, we take it very seriously, even more so now in light of the Connecticut school shootings," Smith said.
On Friday, Adam Lanza, 20, shot and killed 20 children and six adults before killing himself at Sandy Hook Elementary in Newtown, Conn.
Several social media threats led to arrests nationwide since the shootings.
Investigators in Springfield, Ohio, said an 18-year-old man was arrested on Sunday after writing on a Facebook post that he was sick of Connecticut shooting comments and they made him want to shoot kids himself.
A teenager in Columbia, Tenn., was arrested during the weekend after someone posted a message on Facebook saying the person felt like going on a rampage after the Connecticut killings. The 19-year-old suspect remains in jail.
In Los Angeles, the names of the elementary schools and details about the threats were not immediately released.
Detectives and the FBI were still investigating.
The joint investigation has been turned over to Los Angeles police, and there won't be any federal charges, FBI spokeswoman Laura Eimiller said.
When police and FBI agents arrived at the east Hollywood home, the suspect's father gave permission for a search, authorities said.
Nine weapons and ammunition were confiscated, including rifles, a shotgun and handguns, authorities said.
It's not yet known if the weapons belonged to the father or the suspect. No weapons were found at Bangayan's residence in Pomona.
The father's telephone number is unlisted. There is no listing for Kyle Bangayan in Pomona.
The home is in a working-class neighborhood about eight miles northwest of downtown Los Angeles. Pomona is about 30 miles to the east.