Peterson was on campus, armed and in uniform during the shooting, the sheriff said.
"It will be done safely", he said. Only deputies who are trained and qualified will carry those rifles.
Israel also said that "we also need to talk about sensible gun control".
The Broward County Sheriff's Department did not immediately respond to BuzzFeed News' request for additional information.
The practice was implemented Wednesday morning.
"If the weapon is a high caliber, rapid fire assault weapon, it is hard to go into a fight against that if you've got just a handgun".
Coral Springs Police Chief Tony Pustizzi told reporters on Thursday that the confusion stemmed from human error and a "communication failure", not malfunctioning equipment.
New auto allocation seen as key to survival of GM Korea
Outreach efforts will be made to make clear that South Korea's imports of Chinese steel do not target the U.S. market. The union leader said in an interview that he believed in the possibility of GM leaving the country.
The Broward sheriff has said Cruz, after slipping away from the school, casually spent more than an hour drifting through a Walmart store and visiting two fast-food outlets before he was spotted and arrested.
The video shows that Peterson remained outside the building for upward of four minutes during the shooting, which lasted about six minutes, Israel said. "I think it is a awful idea", Nelson said, calling for an assault weapons ban instead.
"He should have went in, addressed the killer, killed the killer", Israel said.
"Our approach to this whole thing is never again".
"Crooked Hillary said that I want guns brought into the school classroom". "My approach to this whole thing is never again, never again, and every decision I make in this investigation is going to be geared towards making sure that I've done everything I possibly can to try and make sure these incidents never happen again".
The Sheriff said in the press conference that Peterson chose to resign his position after being informed on Thursday that he was under investigation and would be suspended without pay. He did not say if Peterson would face criminal charges.
School resource officers are police officers who are responsible for safety and crime prevention in schools, the U.S. government says.