  We present a catalogue of white dwarf candidates selected from Gaia early
data release three (EDR3). We applied several selection criteria in absolute
magnitude, colour, and Gaia quality flags to remove objects with unreliable
measurements while preserving most stars compatible with the white dwarf locus
in the Hertzsprung-Russell diagram. We then used a sample of over 30 000
spectroscopically confirmed white dwarfs and contaminants from the Sloan
Digital Sky Survey (SDSS) to map the distribution of these objects in the Gaia
absolute magnitude-colour space. Finally, we adopt the same method presented in
our previous Gaia DR2 work to calculate a probability of being a white dwarf
(Pwd) for $\simeq$1.3 million sources which passed our quality selection. The
Pwd values can be used to select a sample of $\simeq$359 000 high-confidence
white dwarf candidates in the magnitude range 8< G <21. We calculated stellar
parameters (effective temperature, surface gravity, and mass) for all these
stars by fitting Gaia astrometry and photometry with synthetic models. We
estimate an upper limit of 93 per cent for the overall completeness of our
catalogue for white dwarfs with G $\leq$20 mag and effective temperature
(Teff)>7000K, at high Galactic latitudes (|b|>20{\deg}). Alongside the main
catalogue we include a reduced-proper-motion extension containing $\simeq$10
200 white dwarf candidates with unreliable parallax measurements which could,
however be identified on the basis of their proper motion. We also performed a
cross-match of our catalogues with SDSS DR16 spectroscopy and provide spectral
classification based on visual inspection for all resulting matches.
