“Too many of the legislative proposals being mentioned thus far are driven by politics and have been proven ineffective in the past,” the lawmakers wrote in a letter to Holder on Thursday. “While we do not claim to know everything about gun violence, we do know that a common-sense solution does not involve limiting the constitutional rights of law-abiding citizens. Instead, we should focus on enforcing current law and keeping guns out of the hands of those who shouldn’t have them.”

Since the December shooting in Newtown, Conn., where a gunman killed 20 elementary students, Democratic lawmakers have been calling for stricter gun-control measures -- such as reinstating the assault weapons ban, implementing stricter background checks and banning high-capacity ammunition clips. But Republicans have said those ideas would limit U.S. citizens’ Second Amendment rights and that the key is to keep guns out of the hands of criminals, not law abiding citizens. 

Gowdy and Graham said they’ve discovered that the Department of Justice (DOJ) is prosecuting a fraction of the convicted felons and fugitives who are failing background checks under the National Instant Criminal Background Check System (NICS).

“While we understand that not every denial needs to be prosecuted, every case involving a fugitive from justice or felon in possession of a firearm should be prosecuted to the fullest extent of the law,” the letter stated.

Graham and Gowdy said that in 2010, 76,142 individuals failed a gun purchase background check and that more than 15,000 of those failed background checks were applications from felons and fugitives, who are no longer legally allowed to own a gun. The lawmakers said that only 13 of those cases resulted in guilty pleas.

In the letter, Gowdy and Graham said that if the problem is that the DOJ does not have adequate resources to prosecute these criminals, Congress could assist in identifying funding in the current budget.