We show that the metric multilevel facility location problem is polynomial-time reducible within a factor of 3 to the metric uncapacitated facility location problem. This reduction together with recent approximation algorithms for the latter problem, due to Jain, Mahdian & Saberi, leads to a 4.83-approximation algorithm for the metric multilevel facility location problem and to a 9-approximation algorithm for a capacitated version of it (where facilities have soft capacities). In the class of combinatorial algorithms these performance ratios improve on the previous ones due to Bumb and Kern (6 and 12 respectively).