We have grown Fe films on an epitaxial Pd monolayer on Cu(001) single crystals at room temperature, both Fe and Pd by pulsed laser deposition. The presence of the Pd interlayer influences growth, structure, and magnetism of the Fe films. Up to the thickness of 1.6 ML the Fe films show an out-of-plane easy axis of magnetization which changes to in-plane above. A linear dependence of the longitudinal Kerr rotation on the Fe thickness is obtained despite existing structural transformations. A strong increase of the Curie temperature TC is observed for the Fe films on Pd/Cu(001) compared to the Fe films grown directly on Cu(001). A correlation of the magnetic properties with possible structural changes and the role of Pd monolayer is discussed.