Bush called the shooting in Oregon "heartbreaking," and said he also had challenges that he faced during his tenure as governor of Florida.
"Look stuff happens, there's always a crisis and the impulse is always to do something and it's not always the right thing to do," Bush said at the Conservative Leadership Project in Greenville, South Carolina, referring to taking away rights.
A gunman opened fire on the campus of Umpqua Community College Thursday, killing 9 people and wounding seven others. He later died in a gun battle with police.
The 13 guns he had, including six that he had with him at the school, were all legally purchased, federal officials said today. The guns were either purchased by the shooter or his relatives over the past three years.
President Obama, speaking at the White House, said Bush's remarks didn't deserve a response after a question about them from ABC News' Jonathan Karl.
"I don’t even think I have to react to that one," he said. "I think the American people should hear that and make their own judgments based on the fact that every couple of months we have a mass shooting. And they can decide whether they consider that stuff happening."
Obama reacted emotionally to the shooting during an address Thursday and lamented that mass shootings had become "routine" in the U.S. He also called for greater gun control.
Bush attempted to clarify his comments to reporters after the event and said they were "not related to Oregon."
"Just for clarity here," he said. "Let’s make sure that we don’t allow this to get out of control."
He then defended his comments, adding that tragedies happen all the time and the key is to finding the solution to the deeper issue.
"It wasn't a mistake, I said exactly what I said," Bush said.
The Democratic National Committee has already pounced on the comments, amidst a firestorm of conversation on Twitter, condemning the remarks.
"Americans are killed and injured, families lose their loved ones, and an individual who wants to be the President of the United States shrugs his shoulders and says “stuff happens.” No. The reason this keeps happening is because we let it," said DNC Chair Debbie Wasserman Schultz.
The Bush campaign later shot back that the remarks were "sad and craven" and that Democrats would take Bush's comments out of context to advance their political agenda in the wake of a tragedy.
They also tweeted out out a link to two organizations that are supporting the victims of the mass shooting.