President Barack Obama spoke for the first time since the verdict Friday.
"When Trayvon Martin was first shot, I said that this could have been my son. Another way of saying that is Trayvon Martin could have been me 35 years ago," he said, adding that Florida and other states should review their Stand Your Ground laws.
Scott said the law does more good than harm in Florida.
"We put together a 19 person, bipartisan taskforce and they reviewed it," said Scott. "I agree with them. We should not be changing and I don't support us changing Stand Your Ground."
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Late Thursday, Scott met with some of the protesters who have occupied the capitol for several days. He said he wouldn't call the special session they want on Stand Your Ground.
"I met with these students yesterday up in Tallahassee and here's what I told them: call your legislator, call your house member, call your senator," said Scott. "That's the way the process works in our state, but I believe in our existing Stand Your Ground law."
Rep. Erik Fresen, R-Miami, said the law could be looked at next session.
"As a legislator, at a minimum, we need to, during the regular session, convene, discuss the law, discuss what came out of the citizen group, and perhaps, if necessary, tweak it," he said.
Broward State Attorney Mike Satz, a Democrat, said the law needs more than a tweak.
"Before the passage of Stand Your Ground, you had a duty to retreat before you used deadly forced unless it would put you in greater danger," said Satz. "I really feel that that's the way it should be. They should strike that from the statute."
Trayvon Martin's parents issued a statement thanking President Obama for his comments, saying in part: "We seek a future when a child can walk down the street and not worry that others see him as dangerous because of the color of his skin or the clothes on his back. We seek a future where our children can grow up and become the people God intended them to be."