Both high schools in Middleton, Wisconsin, will be closed on Wednesday after "serious and specific" threats were posted on social media, the school district said Tuesday.

The Middleton-Cross Plains School District didn't disclose the nature of the threats, but it said they were specific to Clark Street Community School and Middleton High School in Middleton, a suburb of Madison, the state capital.

Elementary and middle schools will be open as scheduled "with an increased police presence," it said.

Middleton police confirmed that they were investigating the threats and referred questions to the school district.

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Perry Hibner, a spokesman for the school district, told NBC affiliate WMTV of Madison that the threats were made on Instagram. He said police were working with Instagram to identify the account.

The school district said alert calls were going out to the families of all high school students late Tuesday.

"We realize there will be a lot of speculation and rumors, especially on social media, but at this time there isn't additional information that we can share," it said.