The tour's purpose is to gain public support for enhanced background checks on gun purchasers. Giffords and her husband will travel to all the states where senators have voted against the bill in the past including Nevada, Alaska and Maine.
During their first stop in Las Vegas, the pair, who pride themselves on being gun owners and support the Second Amendment, visited a a gun range where they both shot a weapon for the first time since Giffords was shot in the head during the Tucson, Arizona shooting in January 2011.
In addition the pair met with local leaders at the Latin Chamber of Commerce.
Giffords and Kelly are set to visit Alaska Tuesday on the same day that USA Today published an op-ed piece titled, "Gun rights come with responsibilities" written by the former congresswoman.
"Days before we celebrate our Declaration of Independence and the values that make our nation great, I am taking this week to pay tribute to the Second Amendment -- both the rights it bestows and the responsibilities it requires. Some might consider me an unlikely advocate for gun rights because I sustained terrible injuries in a violent shooting. But I'm a patriot, and I believe the right to bear arms is a definitive part of our American heritage," Giffords wrote.
"We can't stop every person who is determined to do harm, but common-sense measures can prevent tragedies. Expanding background checks will help create a uniform standard for all gun purchases and prevent criminals and the dangerously mentally ill from obtaining powerful weapons."