Mom's Demand Action For Gun Sense in America does not want Target customers to bring firearms into any of the retailer's locations.
According to USA Today the group previously focused gun prevention efforts on Starbucks and Chipotle.
"American moms will not shop where our children and families - including our teens who work at Target - are not safe," the group said in a statement obtained by USA Today.
A spokeswoman for the advocacy group told The Wall Street Journal mothers don't feel safe shopping with their children at the company's locations, where gun advocacates exercise the right to carry a firearm.
"Moms have their eye on Target because it's a place we take our children to shop - and we've been disturbed by some of the demonstrations that gun extremists have held with loaded rifles inside and outside some stores. Assault rifles have no place in the baby aisle," Erika Soto Lamb said.
A Target spokesperson said the retailer keeps customers and employees safe.
"The safety and security of our guests and team members is our highest priority," Molly Snyder said. "Target does not sell firearms or ammunition, and while I do not have information specific to this organization to share, what I can tell you is that Target is committed to following all state and federal laws."
Synder also said the retailer and the advocacy group have not communicated.
The founder of the Mom's group told USA Today that she feels eating establishments and companies should handle gun safety more proactively.
"American businesses and restaurants should not wait for open-carry extremists to demonstrate in their establishments - now is the time to stand up for the safety of employees and customers," Shannon Watts said.
Former New York City Mayor Michael Bloomberg partially sponsors the mom's group.
The organization formed following Dec. 2012's Newtown, Conn., school massacre, The Journal reported.
