Allen made the announcement on Twitter Monday.
The Alliance for Gun Responsibility says Initiative 1639 also would create a background check system similar to the one required for handguns, require completion of a firearms safety course and create standards for safe gun storage.
The group’s initiative effort comes after lawmakers in the Democratic-controlled Statehouse declined to bump the minimum age to buy semi-automatic weapons after the February mass shooting at a Florida high school.
The alliance needs roughly 260,000 petition signatures before the initiative can qualify for the 2018 ballot.
In 2014, Allen donated $500,000 to a successful campaign seeking to expand background checks on gun sales in the state.