Gov. Rick Scott wants armed police officers at every access point outside Marjory Stoneman Douglas High School in Parkland, and he’s willing to send Florida Highway Patrol troopers to the campus to make it happen.

The governor made the offer in a letter Tuesday to Broward Sheriff Scott Israel and School District Superintendent Robert Runcie.

“Recent events at the school have demonstrated the need for additional security measures to be implemented,” Scott said, an apparent reference to Monday’s arrest of Zachary Cruz on trespassing charges.

Cruz, whose brother Nikolas is charged with 17 counts of murder and 17 counts of attempted murder for shooting up the school on Valentine’s Day, is being held in lieu of $500,000 bail.

That the brother of a mass murderer could ride his skateboard onto the campus in broad daylight sent chills throughout the school community.

“Today, I am requesting that immediate action be taken to require an armed law enforcement officer to secure every point of entry at Marjory Stoneman Douglas High School while students are on campus,” Scott said. “To help with this goal, the state is willing to provide assistance from the Florida Highway Patrol, until a more permanent safety plan can be put into place.”

In an interview with the South Florida Sun Sentinel on Tuesday, Israel jumped on the offer.

“Who would turn down help from another agency that wants to help out with the mindset of keeping Broward safe?” he said. “The governor has always been here for Broward County since I’ve been sheriff. I appreciate the offer and I’m looking forward to meeting with the appropriate personnel at the Florida Highway Patrol to integrate the agencies.”

Runcie said he plans to announce Wednesday what he plans to do.

“MSD security continues to be an urgent priority, and we will further enhance school safety measures,” he said.

Also Tuesday, two Marjory Stoneman Douglas students were arrested on charges they brought knives to school and a third was being evaluated for making online threats. A school deputy also was suspended for sleeping on the job after being caught by a student, the Sheriff’s Office said.

Some parents said they have been dissatisfied with the school district’s answers to safety concerns raised since the shooting, pointing to the failure to address Nikolas Cruz’s mental health issues and the trespassing by his brother.

At the city of Parkland’s Education Advisory Board on Monday, board member Wayne Alder called for Runcie and all school board members to resign “so that proper leadership in the district can take place.”

He said the district failed to properly investigate warning signs that Nikolas Cruz was a danger.

Students have said they told authorities that Cruz brought ammunition and knives to school, but there’s no indication of such incidents on disciplinary reports.

“How many other ticking time bombs are left undetected?” asked Alder, whose daughter attends Westglades Middle School, which is adjacent to Stoneman Douglas. “We don’t know and the district doesn’t know. It happened in Parkland this time. Where else is it going to happen?”

In an interview Tuesday, Runcie dismissed the suggestion he resign.

“Resigning isn’t going to stop the fact that guns are readily available,” he said. “Even if we created a fortress around the school, we’ve seen these incidents occur in movie theaters and other venues.

“Start focusing on the real reasons we have these problems: It’s a combination of easy access to guns, and we [as a society] don’t invest in mental health services like we should. I wish they’d come up with real solutions.”

Stoneman Douglas has multiple entry points, including in the front entrance, the staff and student parking lots and the bus loop.

But when school is in session, all but the front entrance are closed. The goal: to boost safety.

The gates are opened in the morning so students can enter, as well as a few minutes before dismissal. They stay open during after-school student activities.

The governor’s offer may ensure troopers are stationed at each entrance even during hours when school isn’t in session.

Runcie said he’s met with every school in Parkland about additional security enhancements and he said “those conversations are going well.”

Broward school officials say they are taking steps to improve security. They are updating projects to enhance security cameras, as well as fencing and gates that limit visitor access to the front office.

However, officials said Stoneman Douglas already had those security measures in place on Feb. 14. Nikolas Cruz arrived about 20 minutes before dismissal, when the gates are opened.

Security cameras were fully functioning. But police had trouble tracking Cruz partly because officers looking at security footage didn’t realize, or didn’t tell their colleagues, the video they were watching was delayed 20 minutes. It caused them to think Cruz was still on campus after he’d already left.

District officials also stressed the need for schools to enforce uniform policies so that outsiders can be more easily recognized. However, Cruz was reportedly wearing a Stoneman Douglas Junior ROTC shirt.