  We use JWST/MIRI MRS spectroscopy of a sample of six local obscured type
1.9/2 active galactic nuclei (AGN) to compare their nuclear mid-IR absorption
bands with the level of nuclear obscuration traced by X-rays. This study is the
first to use sub-arcsecond angular resolution data of local obscured AGN to
investigate the nuclear mid-IR absorption bands with a wide wavelength coverage
(4.9-28.1 $\mu$m). All the nuclei show the 9.7 $\mu$m silicate band in
absorption. We compare the strength of the 9.7 and 18 $\mu$m silicate features
with torus model predictions. The observed silicate features are generally well
explained by clumpy and smooth torus models. We report the detection of the 6
$\mu$m dirty water ice band (i.e., a mix of water and other molecules such as
CO and CO$_2$) at sub-arcsecond scales ($\sim$0.26 arcsec at 6 $\mu$m; inner
$\sim$50 pc) in a sample of local AGN with different levels of nuclear
obscuration in the range log N$_{\rm H}^{\rm X-Ray}$(cm$^{-2}$)$\sim22-25$. We
find a good correlation between the 6 $\mu$m water ice optical depths and
N$_{\rm H}^{\rm X-Ray}$. This result indicates that the water ice absorption
might be a reliable tracer of the nuclear intrinsic obscuration in AGN. The
weak water ice absorption in less obscured AGN (log N$_H^{X-ray}$
(cm$^{-2}$)$\lesssim$23.0 cm$^{-2}$) might be related to the hotter dust
temperature ($>$T$_{sub}^{H_2O}\sim$110 K) expected to be reached in the outer
layers of the torus due to their more inhomogeneous medium. Our results suggest
it might be necessary to include the molecular content, such as, H$_2$O,
aliphatic hydrocarbons (CH-) and more complex PAH molecules in torus models to
better constrain key parameters such as the torus covering factor (i.e. nuclear
obscuration).
