In the event of a DC side fault in modular multilevel converters (MMCs), the fault current contributions are initially made by submodule (SM) capacitor discharge, which occurs before the fault is detected, followed by the AC side contribution to the DC side fault. While the AC side currents can be regulated using fault blocking SMs, the initial discharge of the SM capacitors results in high DC fault currents, which can take several milliseconds to be brought under control. This paper presents a method to actively control the rate of rise of the DC fault current by regulating the discharge of SM capacitors and accelerating the suppression of fault current oscillations during fault ride-through (FRT) in a full-bridge (FB)-MMC system. In the proposed method, the discharge direction of the FBSM capacitors is reversed following the detection of a DC side fault, which leads to a reversal in the fault current direction and a fast drop-off towards the zero-crossing. Immediately after the zero-crossing of the DC fault current, the DC fault is cleared by adjusting the arm voltage references and operating the MMC as a static synchronous compensator (STATCOM) to provide voltage support to the AC grid. The proposed control scheme provides faster fault current suppression, more effective SM capacitor voltage regulation, low AC side and MMC arm current transient peaks, and an overall superior DC-FRT performance compared to methods in which the conventional fault ride-through operation is initiated immediately upon DC fault detection.