  We extend the main result of (G. Badia and G. Olkhovikov. A Lindstr\"om
theorem for intuitionistic propositional logic. Notre Dame Journal of Formal
Logic, 61 (1): 11--30 (2020)) to the first-order intuitionistic logic (with and
without equality), showing that it is the maximal (with respect to expressive
power) abstract logic satisfying a certain form of compactness, the Tarski
union property and preservation under asimulations. A similar result is also
shown for the intuitionistic logic of constant domains.
