Investors have 30 days to decide if they want to take up the offer, though many are expected to do so. As recently as last month, California’s treasurer publicly urged the state teacher pension fund to sell its 2.5 percent stake in the gun manufacturer.

A spokesman for Cerberus declined to comment.

Cerberus first entered the gun business by buying Bushmaster Firearms seven years ago. The private equity firm — named after the multiheaded dog that guarded the gates of the Greek underworld — then bought a number of other gun manufacturers, including the nearly two-century-old Remington Arms, the country’s oldest firearms maker.

The move was a characteristically bold and tough-minded one by Cerberus, which made its name wading into deals that others feared. It first rose to prominence by investing in the debt of distressed companies, an often bare-knuckled business where fighting over cents on the dollar is the norm.

The company’s founder, Stephen A. Feinberg, has shown a particular affinity for investments tied to the military. He is an avid hunter whose preferred firearm is a Remington 700 rifle.

Through that string of deal-making, the firm built up what became known as the Freedom Group into the country’s biggest firearms maker, with 3,200 employees and sales in more than 60 countries.

Yet the Sandy Hook shooting eventually prompted Cerberus to try to retreat from the business — an unusual instance of a Wall Street firm bowing to social concerns over one of its investments. The firm was affected by the tragedy on a more personal level as well, since Mr. Feinberg’s father was a resident of Newtown at the time.

“We believe that this decision allows us to meet our obligations to the investors whose interests we are entrusted to protect without being drawn into the national debate that is more properly pursued by those with the formal charter and public responsibility to do so,” the firm said in announcing a sales process for Remington.