FAIR LAWN, N.J. (CBSNewYork) — Threats were made against several school districts in Bergen and Passaic counties Tuesday and some law enforcement officials are pushing for tougher rules against those responsible.

The threats were received at schools in Clifton, Bergenfield, Leonia, Tenafly, Teaneck, Garfield, Fair Lawn, Hackensack and Englewood.

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Police said the threats were left on school voicemails overnight, claiming a bomb was somewhere in the school and that a mass shooting would take place, CBS2’s Christine Sloan reported.

Sources said they believe the messages were left by the same person, Sloan reported.

None of the threats were deemed to be credible, police said.

Some schools were placed on lockdown while others were evacuated, forcing students out into the bitter cold.

Leonia High School was placed on lockdown, which has since been lifted.

Fair Lawn High School students were moved to Memorial Middle School around 9 a.m. Tuesday.

“My teacher said, ‘Go get your coats and then come back here and we’ll all go down together,'” one student said. “I got my coat and by the time I was trying to go back they were just, ‘No, get out,’ that’s all they were saying.”

“It was very scary,” one parent said. “You’re always concerned for your kids. You don’t know what’s going to happen, you hear all these crazy things throughout the country.”

Students have since returned to Fair Lawn High School , where there is a strong police presence.

Bergenfield High School was also evacuated and many students didn’t even have time to grab their coats, WCBS 880’s Marla Diamond reported.

“It was just in the middle of the period, in the middle of class,” said 16-year-old Kenny Garcia, who was given a blanket by a first responder. “It was like, ‘Oh, everybody’s got to get up and leave.'”

“It was scary,” said 10th grader Luis Vargas. “I think some girl fainted.”

Parents received a reverse 911 call about the evacuation, and many raced to the school to check on their kids.

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Police resources were stretched thin for many hours in multiple towns.

The Bergen County Sheriff’s Department responded to Bergenfield High School with bomb-sniffing dogs.

“We have to take each and every single call as serious in nature,” said Bergenfield Police Capt. Mustafa Rabboh. “When we go to incidents like this it takes us away from other calls that are potentially life threatening.”

Clifton police sent plain clothes detectives as well as K-9 units throughout the school district as a precautionary measure.

Callers also threatened law enforcement.

“One or two of the calls were when police respond there’s going to be the shooting of law enforcement,” Bergen County Sheriff, Michael Saudino said.

The sheriff said the threat, a robotic call with a California caller ID, could have been locally.

“My hope is that federal legislators will look at these things. It’s time to stop the protection of some of these companies hiding the identity of people who are doing these types of calls,” Saudino said.

Authorities said an example will be made of the person responsible, because everyone was put at risk and it cost the taxpayers thousands of dollars.

“With digital or online crimes there are digital fingerprints and we will follow up on each and every lead,” acting Bergen County Prosecutor, Gurbir Grewal said.

Parents were happy it wasn’t worse.

“It was very scary, happening around the country,” Heather Berletti said.

As a precaution police will keep a strong presence at all of the schools.

Schools in Bergen County have different protocols when it comes to threats, which is why some schools were evacuated and others went into lockdown.

Police said they knew early on the threats were not credible because there was a similar threat in 2014.

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They are not sure if today’s threat is connected.