Ćirić and Presić [Acta Math. Univ. Comenian. LXXVI (2) (2007), 143-147] extended the notion of Presić contraction to kth-order Ćirić type contractive mappings on a metric space. In this paper,we extend the concept of Ćirić-Presić to Jleli-Samet- Ćirić-Presić contractive mappings and obtain some related fixed point theorems. Our results generalize some known ones in the literature. A real concrete example and an illustrating application are given in support of our main result