We present a new analysis of the first mid-infrared N-band long-baseline interferometric observations of an extragalactic source: the nucleus of the Seyfert 2 galaxy NGC 1068, obtained with MIDI (Mid-InfrareD Interferometer), the mid-infrared beamcombiner at the European Southern Observatory (ESO) Very Large Telescope Interferometer (VLTI). The resolution of $\lambda/B \sim 10$ mas allows us to study the compact central core of the galaxy between 8 and 13 μm. Both visibility measurements and MIDI spectrum are well reproduced by a simple radiative transfer model with two concentric spherical components. The derived angular sizes and temperatures are ~35 and 83 mas, and ~361 K and 226 K for these two components respectively. Other evidence strongly supports such low temperatures. This modeling also provides the variation of optical depth as a function of wavelength for the extended component across the N-band suggesting the presence of amorphous silicate grains. This shows that MIDI has carried out the first direct observations of the distribution of dust around the central engine.