According to general relativity, the cosmological redshift can be caused also by another mechanism, similar to the gravitational redshift of massive stars - in principle due to differences in the global metric field between a source in the past and an observer in the present. In this paper, we analyse spacetime using a fully conformal metric, where the character of natural physical time is preserved and the scaling factor acts identically on all four spacetime coordinates. Unlike the Robertson-Walker metric, the fully conformal metric preserves the time independence of the speed of light and energy-momentum tensor. The motivation was to test the possibility of the above cosmological redshift mechanism in confrontation with astrophysical data. Probably the most important consequence is the generalized formulation and interpretation of the Hubble-Lemaître law z(r) = (eHr/c — 1), which shows good agreement with astrophysical data even for farthest supernovae. Confronting the model of conformal metric with some astrophysical data shows an interesting agreement with the observed spatial distribution of astrophysical sources such as γ-ray bursts and quasars. On a cosmological scale, the fully conformal metric mentioned above naturally determines global energy density, spatial flatness, and solves the horizon problem and Olbers' paradox in infinite spacetime.