  We present ALMA Band 6 $^{12}$CO(2--1) line and rest-frame 232GHz continuum
observations of the nearby Compton-thick Seyfert galaxy NGC5643 with angular
resolutions 0.11-0.26arcsec (9-21pc). The CO(2--1) integrated line map reveals
emission from the nuclear and circumnuclear region with a two-arm nuclear
spiral extending 10arcsec on each side. The circumnuclear CO(2--1) kinematics
can be fitted with a rotating disk, although there are regions with large
residual velocities and/or velocity dispersions. The CO(2--1) line profiles of
these regions show two different velocity components. One is ascribed to the
circular component and the other to the interaction of the AGN outflow, as
traced by the [O III]5007AA emission, with molecular gas in the disk a few
hundred parsecs from the AGN. On nuclear scales, we detected an inclined
CO(2--1) disk (diameter 26 pc, FWHM) oriented almost in a north-south
direction. The CO(2--1) nuclear kinematics can be fitted with a rotating disk
which appears to be tilted with respect to the large scale disk. There are
strong non-circular motions in the central 0.2-0.3 arcsec with velocities of up
to 110km/s. In the absence of a nuclear bar, these motions could be explained
as radial outflows in the nuclear disk. We estimate a total molecular gas mass
for the nuclear disk of $M({\rm H}_2)=1.1\times 10^7\,M_\odot$ and an H$_2$
column density toward the location of the AGN of $N({\rm H}_2)\sim 5 \times
10^{23}\,{\rm cm}^{-2}$, for a standard CO-to-H$_2$ conversion factor. We
interpret this nuclear molecular gas disk as the obscuring torus of NGC5643 as
well as the collimating structure of the ionization cone.
