The device comprises two gripping arms movable to and from a resting position and a gripping position in which they are spread apart from one another and in contact with an inside face of the side wall of the cooking vessel; a fix-mounted gripping member designed for being in contact with an outside face of the side wall of the cooking vessel; and displacement means designed for being manually guided to and from an open position and a closed position and for effecting a spreading of the movable arms while switching from the open position to the closed position. Said device further comprises anti-return means separate from the displacement means and designed for being moved from a resting position to a clamping position in which they are inserted between the two arms and prevent the two arms from coming together.