I've seen studies that suggest this to be true, and others that suggest it is false. The process of collecting gun crime stats is so complex, and the US gun lobby so powerful, that it's hard to decipher what goes on in the US where guns are concerned.
What we DO know, however, is that there are more guns per person in the US than in any other nation (
around 9 guns for every 10 people) and that the US has some of the highest levels of gun murder and gun suicide in the western world.
I don't pretend to know the answers, or to even fully understand the US gun debate, but 30,000 dead Americans every year tell a damning story. Considering your Government can spend trillions of dollars to rescue banks and car companies from going broke, I'd suggest a billion dollar programme to register gun ownership and gun capability would be a small price to save even one tenth of those lives each year.