Primal algebras have been generalized in various ways. Many of these generalized notions are defined by requiring that every function which is compatible with some kind of related structures of the algebra (e.g., subalgebras, congruences, automorphisms, isomorphisms between subalgebras) must be a term function. In the present paper the authors introduce a further notion of this kind: the case when the related structure to be considered is the endomorphism monoid. Accordingly the authors define an algebra to be endoprimal if every function in it which commutes with all endomorphisms is a term function. The authors give a full description of endoprimal distributive lattices.