The main objective of this work is to extend a pressure-based algorithm capable of solving both incompressible and high compressible flow regimes. Essentially, the density plays the primary role in high density-variation fields and the pressure is assumed to display a passive role via the equation of state. Contrary to the density variable, the pressure dependent variable provides a smooth transition for solving either low-density variation or constant-density fields. In the current work, a new pressure-based algorithm is suitably developed in order to achieve the advantages of both the pressure-based and the density-based algorithms. The chosen dependent variables play a significant role in achieving dual benefits. The performance of the extended algorithm is then investigated within a convergent-divergent nozzle flow which represents a broad range of compressibility within a single test. The investigation shows that the extended pressure-based algorithm demonstrates excellent performance for solving full range of subsonic Euler flow regime, from pseudo-compressible to transonic regimes. This robust performance can be considered as a major contribution in solving heat transfer problems with high density variation.