Schools in the North Lakes area of Queensland remain open and police say overt and other operations are enough to keep students and staff safe.
But they also said they had to treat the threats - posted on two social media platforms - seriously.
Soon after police addressed the media, officers confirmed a bomb threat had forced the evacuation of a building in North Lakes, but it was not a school.
Officers swept the building and people were allowed to return after about 30 minutes.
One of the posts featured images of US students Dylan Klebold and Eric Harris who killed 12 pupils and a teacher at Columbine High School in Colorado in April 1999 and threatened a worse shooting at North Lakes.
File: 1998 yearbook photos from Columbine High School in Littleton, Colo., of Dylan Klebold and Eric Harris. Source: AAP
"A school in North Lakes QLD is going to get professionally shot up with as many casualties as possible,” the post published on forum 4chan read.
"Don't come to school next week," it warned.
Acting Chief Superintendent Chris Stream said overt and other police operations were underway, including increased patrols in the area.
But he also said there was no other intelligence to suggest the threats were credible, and parents could have confidence that their children were safe at school.
"Students attending those schools are safe with the current activities we are undertaking," he said.
"We take all threats of this type very, very seriously."
No specific schools were named in the posts, which also made reference to the recent shooting that killed 17 people at a school in Parkland, Florida.
The education department has written to parents in the area advising them of the situation, but saying schools remain open given there was "no credibility to any specific threat".
Police want to hear from anyone who knows anything about the posts and said people should remain vigilant.
