I think the quickest and most powerful step we could take to reduce gun violence is to end the war on drugs. This lucrative black market is very violent and leads to a large percentage of our gun murders in America, either by direct effects (such as drug/gang violence), or secondary effects such as turning non-violent drug offenders violent in prison and then releasing them into communities where they commit violence, or tertiary effects such as being raised within a violent community filled with drug gangs and violent drug offenders.
By no means is this a perfect solution, but I think it would lead to a large and almost immediate reduction in gun violence. I don't see this as a final step, but it would be a great first step.