Stretchable and flexible devices are being widely developed for the application of modern electronics to biological systems which are soft, elastic, and curved. However, stretchable and flexible electromagnetic and/or magnetic devices are relatively rare, regardless of their importance in many electromechanical systems. Therefore, this study develops a fully stretchable electromagnet using a metallic coil and a magnetoactive polydimethylsiloxane (PDMS) sponge embedded with iron microparticles. In a cylindrical prototype, the magnetoactive PDMS sponge acts as a ferromagnetic core of the electromagnet, enhancing the magnetic fields to ~ 300% of that of a control device without the iron microparticles. The microscale pores of the PDMS sponge and the spring structures of the metallic coil enable the elongation of the electromagnet up to ~ 115%. Similarly, we fabricated and experimentally characterized a patch-shaped prototype of a fully stretchable electromagnet, and discussed its practical limitations.