This paper presents a modified version of the hybrid FEM-DBCI (Finite Element Method-Dirichlet Boundary Condition Iteration) method to solve static and quasi-static electromagnetic field problems in open boundary domains. The modification consists of overlapping the fictitious truncation boundary with the integration one, as in the FEM-BEM (Boundary Element Method) method. The global algebraic system obtained is solved iteratively by means of the GMRES (Generalized Minimal Residual) solver, applied virtually to a reduced system in which the unknowns are those relative to the potential on the truncation boundary only. Some validation examples are provided.