Context. The mechanism behind the shaping of bipolar planetary nebulae is still poorly understood. It is becoming increasingly clear that the main agents must operate at their innermost regions, where a significant equatorial density enhancement should be present and related to the collimation of light and jet launching from the central star preferentially towards the polar directions. Most of the material in this equatorial condensation must be lost during the asymptotic giant branch as stellar wind and later released from the surface of dust grains to the gas phase in molecular form. Accurately tracing the molecule-rich regions of these objects can give valuable insight into the ejection mechanisms themselves. Aims: We investigate the physical conditions, structure and velocity field of the dense molecular region of the planetary nebula NGC 6302 by means of ALMA band 7 interferometric maps. Methods: The high spatial resolution of the 12CO and 13CO J = 3-2 ALMA data allows for an analysis of the geometry of the ejecta in unprecedented detail. We built a spatio-kinematical model of the molecular region with the software SHAPE and performed detailed non-LTE calculations of excitation and radiative transfer with the shapemol plug-in. Results: We find that the molecular region consists of a massive ring out of which a system of fragments of lobe walls emerge and enclose the base of the lobes visible in the optical. The general properties of this region are in agreement with previous works, although the much greater spatial resolution of the data allows for a very detailed description. We confirm that the mass of the molecular region is 0.1 M⊙. Additionally, we report a previously undetected component at the nebular equator, an inner, younger ring inclined 60° with respect to the main ring, showing a characteristic radius of 7.5 × 1016 cm, a mass of 2.7 × 10-3M⊙, and a counterpart in optical images of the nebula. This inner ring has the same kinematical age as the northwest optical lobes, implying it was ejected approximately at the same time, hundreds of years after the ejection of the bulk of the molecular ring-like region. We discuss a sequence of events leading to the formation of the molecular and optical nebulae, and briefly speculate on the origin of this intriguing inner ring. The model file (in SHAPE format) is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A27