In Wednesday's letter, Lozancic ironically proposed that Ashdown should explain his intentions to manage the "personnel" of national parties dominating in the state and two entities' parliaments despite election results.
Ashdown said Lozancic was a good entity president but that he would do better as a comedy writer.
Ashdown removed Covic on Tuesday after the Court of Bosnia-Herzegovina confirmed an indictment charging him with corruption and economic crimes.
The Briton made the decision following demands from the international community, notably the US.
He declined to tell the Banja Luka press anything about the announced rehabilitation of Serb politicians he removed last summer on suspicion that they had been helping harbour Hague war crimes tribunal indictees.