Singularly perturbed partial differential equations occur in many practical problems. These equations are characterized mathematically by the presence of a small parameter ϵ multiplying to one or more of the highest derivatives in a partial differential equation. Finding stable approximate solutions to such problems is mathematically challenging and interesting due to the fact that the solution is not stable as ϵ goes to 0. Many numerical schemes have been explored in the literature for finding approximate solutions to such PDEs. However, in this paper, our attempt is to propose a regularized iterative scheme as an alternative approach for finding stable approximate solutions to singularly perturbed elliptic and parabolic PDEs. We propose a general theoretical frame work for unbounded operators and then apply it for solving both singularly perturbed parabolic and elliptic PDEs. Theoretical results are illustrated through numerical examples and compared with other standard schemes. Numerical investigation assert that the proposed scheme is a very competitive and an alternate approach for solving the singularly perturbed problems.