A setting tool for actuating a downhole component includes an inner tubular configured to be connected in fluid communication with a borehole string, a housing configured to define a first fluid chamber and a second fluid chamber isolated from the first fluid chamber and in fluid communication with the inner tubular, and a setting piston in pressure communication with the second fluid chamber. The setting tool includes a metering module coupled to the housing and disposed at an end of the first fluid chamber, the metering module including a fluid path forming a restriction therein, and an outlet connected to the fluid path. The outlet is configured to be opened to permit fluid to flow out of the first chamber at a controlled rate to generate a differential pressure between the first and second chambers that causes the setting piston to apply a gradually increasing force on the component.