Context. With infrared interferometry it is possible to resolve the nuclear dust distributions that are commonly associated with the dusty torus in active galactic nuclei (AGN). The Circinus galaxy hosts the closest Seyfert 2 nucleus and previous interferometric observations have shown that its nuclear dust emission is particularly well resolved. Aims. The aim of the present interferometric investigation is to better constrain the dust morphology in this active nucleus. Methods. To this end, extensive new observations were carried out with the MID-infrared Interferometric instrument (MIDI) at the Very Large Telescope Interferometer, leading to a total of 152 correlated flux spectra and differential phases between 8 and 13 μm. To interpret this data, we used a model consisting of black-body emitters with a Gaussian brightness distribution and with dust extinction. Results. The direct analysis of the data and the modelling confirm that the emission is distributed in two distinct components: a disk-like emission component with a size (FWHM) of ~0.2 × 1.1 pc and an extended component with a size of ~0.8 × 1.9 pc. The disk-like component is elongated along PA ~ 46° and oriented perpendicular to the ionisation cone and outflow. The extended component is responsible for 80% of the mid-infrared emission. It is elongated along PA ~ 107°, which is roughly perpendicular to the disk component and thus in polar direction. It is interpreted as emission from the inner funnel of an extended dust distribution and shows a strong increase in the extinction towards the south-east. We find both emission components to be consistent with dust at T ~ 300 K, that is we find no evidence of an increase in the temperature of the dust towards the centre. From this we infer that most of the near-infrared emission probably comes from parsec scales as well. We further argue that the disk component alone is not sufficient to provide the necessary obscuration and collimation of the ionising radiation and outflow. The material responsible for this must instead be located on scales of ~1 pc, surrounding the disk. We associate this material with the dusty torus. Conclusions. The clear separation of the dust emission into a disk-like emitter and a polar elongated source will require an adaptation of our current understanding of the dust emission in AGN. The lack of any evidence of an increase in the dust temperature towards the centre poses a challenge for the picture of a centrally heated dust distribution.