In this paper, we propose a distributed algorithm to solve multi-agent constrained optimization problems. Specifically, we employ the recently developed Accelerated Distributed Augmented Lagrangian (ADAL) algorithm that has been shown to exhibit faster convergence rates in practice compared to relevant distributed methods. Distributed implementation of ADAL depends on separability of the global coupling constraints. Here we extend ADAL so that it can be implemented distributedly independent of the structure of the coupling constraints. For this, we introduce local estimates of the global constraint functions and multipliers and employ a finite number of consensus steps between iterations of the algorithm to achieve agreement on these estimates. The proposed algorithm can be applied to both undirected or directed networks. Theoretical analysis shows that the algorithm converges at rate $O(1/k)$ and has steady error that is controllable by the number of consensus steps. Our numerical simulation shows that it outperforms existing methods in practice.