Provo, Utah (CNN) Mitt Romney said Friday that the nation must act swiftly to address the scourge of gun violence, stating that he was open to tougher measures like "enhanced background checks" if they would help keep guns out of the hands of the mentally ill.

"What happened is unthinkable and unimaginable," he said after offering prayers for the victims of the Florida shooting. "We must take action to prevent tragedies like this from happening again."

Speaking at a fundraising dinner held by Utah County Republicans in his first official appearance as a U.S. Senate candidate, Romney said he hoped to see the state generate innovative solutions for stopping school shootings, rather than the federal government.

Romney did not endorse any one legislative solution, noting that none of the federal legislation that he's read would have prevented the tragedy. One possible exception, he said, is the legislation that retiring Utah Sen. Orrin Hatch has proposed for enhanced background checks before gun purchases.

Speaking to reporters after the event, however, Romney said he had not yet studied that legislation -- and would hold off from endorsing it until he'd had a chance to do so.

Read More