NELSON, Ga. (AP) -- A group that supports gun control filed suit Thursday against a north Georgia town that recently passed a law requiring gun ownership that it said is mostly symbolic.

The Washington-based Brady Center to Prevent Gun Violence filed a federal lawsuit against the town of Nelson, about 50 miles north of Atlanta, claiming the law is unconstitutional. The suit contends the Second Amendment doesn't require anyone to have a gun, and government cannot require citizens to arm themselves.

"Forcing residents to buy guns they do not want or need won't make the city of Nelson or its people any safer, and only serves to increase gun sales and gun industry profits," Jonathan Lowy of the Brady Center said in a statement.

City manager Brandy Edwards said town leaders had not seen the lawsuit and had no immediate comment.

Council members passed the ordinance April 1 requiring every head of household in the town of 1,300 to have a gun and ammunition, but there are exceptions. The law exempts anyone who opposes gun ownership or has certain disabilities.

City leaders said the law was mostly symbolic, isn't being enforced and includes no penalty.

Supporters of the law say light police patrols leave city residents virtually unprotected for most of the day.

The lawsuit contends violators are subject to a fine of as much as $1,000, but Edwards said that is incorrect.

Supporters of the law said they wanted to make a statement about gun rights at a time when President Barack Obama and others were seeking restrictions after the shooting that killed 20 children and six adults at an elementary school in Connecticut in December.

The proposed ordinance is similar to a law that passed in Kennesaw in 1982 and other towns in the U.S. have considered such measures.