We propose a new primal-dual algorithm for solving nonlinearly constrained minimization problems. This is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing an augmented Lagrangian and a log-barrier penalty to handle both equality and bound constraints. Two kinds of iterations are used. The outer iterations at which the different parameters, such as the Lagrange multipliers and the penalty parameters, are updated. The inner iterations to get a sufficient decrease of a given primal-dual penalty function. Both iterations use the same kind of coefficient matrix and the corresponding linear system is solved by means of a symmetric indefinite factorization including an inertia-controlling technique. The globalization is performed by means of a line search strategy on a primal-dual merit function. An important aspect of this approach is that, by a choice of suitable update rules of the parameters, the algorithm reduces to a regularized Newton method applied to a sequence of optimality systems derived from the original problem. The global convergence and the asymptotic properties of the algorithm are presented. In particular, we show that the algorithm is q-superlinear convergent. In addition, this method is able to solve the well known example of Wachter and Biegler, for which some interior point methods based on a line search strategy fail.