We apply a statistical deconvolution of the parallax errors based on Lucy's inversion method (LIM) to the Gaia DR3 sources to measure their 3D velocity components in the range of Galactocentric distances R between 8 and 30 kpc with their corresponding errors and rms values. We find results that are consistent with those obtained by applying LIM to the Gaia DR2 sources, and we conclude that the method gives convergent and more accurate results by improving the statistics of the data set and lowering observational errors. The kinematic maps reconstructed with LIM up to R ≈ 30 kpc show that the Milky Way is characterized by asymmetrical motions with significant gradients in all velocity components. Furthermore, we determine the Galaxy rotation curve V C (R) up to ≈27.5 kpc with the cylindrical Jeans equation assuming an axisymmetric gravitational potential. We find that V C (R) is significantly declining up to the largest radius investigated. Finally, we also measure V C (R) at different vertical heights, showing that, for R < 15 kpc, there is a marked dependence on Z, whereas at larger R the dependence on Z is negligible.