PORTLAND — Police are investigating a rumor spread on Facebook that someone intends to do harm in high schools in Cumberland and York counties on Dec. 21, a school official announced Wednesday.

Portland Public Schools Superintendent Emmanuel Caulk released a statement to the media after a meeting was held involving high school principals, school district leaders and the Portland Police Department to review security measures for schools.

“Although the message does not refer specifically to the Portland Public Schools and we have no evidence that the threat is real, we are taking every precaution to protect our students and staff,” Caulk said in his statement.

He added that police have not confirmed the authenticity of the message, but are investigating.

In the wake of last week’s school shooting in Newtown, Conn., many have been on edge, said Lt. Jim Sweatt of the Portland Police Department.

“It’s upset everyone, from police officers to young children,” Sweatt said Wednesday evening.

Lt. Chris Sanborn of the Gorham Police Department said the rumors did not refer to a specific threat or target but were focused “somewhere between York and Gorham in Cumberland and York county areas.”

Sanborn said his department has been in contact with other law enforcement agencies in its investigation.

Gorham police will step up patrols at its schools for the next two days, he said.

“We’ve added some additional staff for the next couple of days for the safety of our community and our schools,” said Sanborn.

Portland police will be doing the same thing, said Sweatt.

“We know in our community that school safety is important. We’ll be increasing our physical presence to provide that security,” said Sweatt. “We’re trying to bring a sense of security to our schools and community.”

Caulk said in his statement that Deering and Portland High Schools will continue to have a full-time police officer on site. Casco Bay High School and Portland Arts and Technology High School will have a police officer on Friday.

“We take seriously any and all threats and work with police to investigate them appropriately,” Caulk said.

He added that last week’s school shooting has been difficult for students, parents and staff.

“In these days, specifically after the incident in Connecticut, you have to play it safe,” said Sanborn. “We’re certainly working tediously to follow up on leads. Hopefully, if there is something, we’re able to avert it.”