A metal cord has an M+N construction with two concentric layers. An internal first layer or core includes M wire(s) of diameter d1, M having a value from 1 to 4. An external second layer includes N wires of diameter d2 and is positioned around the core, the N wires being wound in a helix. Between the wires of the two layers are gaps, some or all of which include a filling rubber based on an unsaturated thermoplastic elastomer. The filling rubber may be, for example, based on an SBS or an SIS block copolymer. When used in a molten state, the thermoplastic elastomer presents no problem due to unwanted stickiness if the filling rubber overspills outside the cord after manufacture. The unsaturated and therefore (co)vulcanizable nature of the thermoplastic elastomer makes it compatible with diene rubber matrices used as calendering rubber in metal fabrics intended for reinforcing tires.