Embodiments of a method and a system for recovering a metal, such as uranium, from a metal-containing material are disclosed. The metal-containing material is exposed to an extractant containing a liquid or supercritical-fluid solvent and an acid-base complex including an oxidizing agent and a complexing agent. Batches of the metal-containing material are moved through a series of stations while the extractant is moved through the stations in the opposite direction. After the extraction step, the metal is separated from the solvent, the complexing agent and/or other metals by exposing the extract to a stripping agent in a countercurrent stripping column. The complexing agent and the solvent exit the column and are separated from each other by reducing the pressure. The recovered complexing agent is recharged with fresh oxidizing agent and recombined with fresh or recovered solvent to form a recovered extractant, which is distributed through the extraction stations.