City officials said they have paid out more than $22,000 in the exchanges since the program started Dec. 23, CNN reported.
Mayoral spokeswoman Elaine K. Ficarra said the money to buy the guns has mostly come from private donations. A total of nearly $100,000 has been raised, The Bridgeport News reported.
City officials said they plan to hold gun buyback events every weekend until the money runs out.
"These guns could have created victims," Bridgeport Mayor Bill Finch said. "We know if we can reduce the number of weapons that are available through breaking into people's houses and grabbing guns, we are a safer society."
Meanwhile, in Newtown, Conn., where Adam Lanza shot and killed 26 people, including 20 children, at the elementary school before turning his gun on himself, police say they may re-create the scene outside the Sandy Hook Elementary School, The Hartford (Conn.) Courant reported.
Police are trying to determine whether Lanza shot at police or not.