Method for manufacturing glass containers (30) having thin lateral walls (31) and a mouth (32) narrower than the body defined by said lateral walls, comprising at least one step of mould forming by introducing blown air into a glass hollow body blank within the mould, wherein said glass body is supported in the mould by means of a neck ring (41) that can be opened, suitable for realization of the mouth (32) of the container (30) and consisting of a plurality of circumferential sectors (44) that can be moved away from each other, the method further comprising a step of opening the neck ring (41) at the end of the mould forming step, wherein each circumferential sector (44) performs, starting from a closed position of the neck ring (41), in which the circumferential sectors (44) are coplanar and form a substantially continuous annular element provided with a central axis (45), a first radial translation movement, in said coplanar configuration, moving away from the axis (45) of said annular element, followed by a second rotation movement of each circumferential sector (44) around a respective axis (46) directed perpendicular to the direction of the axis (45) of said annular element, up to an open position of the neck ring (41), wherein the circumferential sectors (44) are rotated out of said coplanar configuration, moving away from each other, around said axes (46) directed perpendicular to the direction of the axis (45) of said annular element.