Speaking to CBS 17 in Wilson, the North Carolina Republican responded to questions about tighter gun legislation in the wake of the shooting at a high school in Parkland, Florida, in February.
“There are areas of great common agreement that we can find: bump stocks are certainly one of them, age, background checks,” he said.
Several lawmakers have proposed raising the age requirement to buy some weapons and some state legislatures are addressing age limits. Burr said that age restrictions should be left to states.
The Justice Department last month announced a regulation that would effectively ban bump stocks, classifying them as a machine gun, which are already banned by federal law.
GOP Sen. Tim Scott said over the weekend on CBS that an ban on bump stocks would “fly through Congress tomorrow.”
Burr said Tuesday “Anywhere that we can get agreement in Congress, and there’s no infringement on the Second Amendment, I think this Congress is willing to lay on the table and talk about.”
Burr also responded to criticism that the National Rifle Association spent $5.5 million against Burr’s Senate opponents, according to the Center for Responsive Politics, the second-highest amount behind Sen. John McCain.
Burr said that the money did not mean he was subject to the whim of the NRA.
“One is only susceptible to lobbying if they’re weak and they trust what an individual tells them without verification,” he said. “I can’t influence or impact where the NRA goes and spends money. And, if they spend it in North Carolina, somehow that accounts because I’m up for re-election, that it counts towards me.”
Watch: Blumenthal and Graham Discuss New Gun-Control Measure