A suture needle driving instrument comprises a shaft and an end effector. The end effector is located at the distal end of the shaft and includes a pair of needle grasping arms. Each grasping arm extends along a respective arm axis. The grasping arms are operable to drive a suture needle along a rotational path about an axis, such as one of the arm axes, that is offset from the central longitudinal axis of the shaft. The rotational path may be perpendicular to the axis of the shaft. A needle driven by the end effector may have an arc radius that is greater than the radius of the shaft. At least one of the needle grasping arms may include a dogleg feature positioning a distal portion of the grasping arm outside the radius of the shaft. The instrument may be used through a trocar during minimally invasive surgery.