Update: According to the governor's office, the Broward County Sheriff's Office accepted the state's offer and eight highway patrol troopers will report to Marjory Stoneman Douglas High School on Thursday.

Gov. Rick Scott said Tuesday the state is offering to send highway patrol troopers to secure every point of entry at Marjory Stoneman Douglas High School in Parkland, following several student arrests the same day the school's officer was suspended for allegedly sleeping on the job.

Scott sent a letter to Broward County Sheriff Scott Israel and Broward Superintendent Robert Runcie Tuesday afternoon, saying he had heard from Parkland parents.

"Today, my office heard from parents of students at Marjory Stoneman Douglas High School, including parents who lost their children during the February attack," the letter read. "They are still concerned about student safety at the school. Recent events at the school have demonstrated the need for additional security measures to be implemented."

Scott's move came after the Broward Sheriff's Office suspended one of the deputies it had assigned to a security shift at Marjory Stoneman Douglas High School Tuesday, after a student there caught him sleeping in his patrol vehicle parked next to the building where the shooting occurred.

BSO Deputy Moises Carotti was suspended with pay until an internal affairs investigation and was forced to turn in his badge and marked police vehicle. He is also required to inform the office's internal affairs department of his location twice a day.

The sheriff's office also said two Stoneman Douglas students were arrested Tuesday for carrying weapons on campus. One student pulled a knife out of her bra after a lunchtime fight and the other was charged after a teacher was told he had displayed a knife on a bus the day before.

A third student was charged with a misdemeanor after detectives say he made a threat on social media.

In the letter, Scott instructed the two Broward officials to let his office know what is needed from Florida Highway Patrol "by the end of the week," saying it would be a temporary measure "until a more permanent safety plan can be put into place."

Miami Herald Tallahassee bureau reporter Elizabeth Koh contributed.