BARCELONA—Spanish Prime Minister Mariano Rajoy set a Monday deadline for Catalonia’s leader to clarify whether he declared independence, taking the first step toward potentially stripping the region of some of its powers and escalating his confrontation with the separatists.

Mr. Rajoy on Wednesday accused the separatist leader Carles Puigdemont of deliberately sowing confusion the prior night by declaring the region an independent republic based on the results of an unauthorized referendum, but immediately asking lawmakers...