Washington (CNN) 2020 Democratic presidential candidate Kirsten Gillibrand suggested she supports a mandatory national buyback program for assault weapons and that she would be open to criminal prosecution for those who don't sell back their firearms.

"I think we should ban assault weapons as well as large magazines. As part of passing that ban, do a buyback program across the country so that those who own them can be compensated for the money they spent," Gillibrand, a Democratic senator from New York, told CNN's Poppy Harlow on Wednesday.

Democrats have dropped the cautious rhetoric on gun control in the aftermath of a pair of mass shootings, a little more than 12 hours apart, in El Paso, Texas, and in Dayton, Ohio, earlier this month. But they have been split over whether a buyback program implemented by the federal government should be mandatory or voluntary.

Pressed on whether the program should be mandatory, Gillibrand replied, "You don't want people to retain them because if you make them illegal, you don't want to grandfather in all the assault weapons that are all across America."

"You would like people to sell them back to the government, so that you can make sure people who shouldn't have access to these weapons couldn't have them," Gillibrand added.