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We fabricated multicore MgB2/Fe wires with much higher packing density and J c than powder-in-tube (PIT)-processed wires by internal Mg diffusion (IMD). Mg cores in the composite were uniformly cold worked into fine filaments by room-temperature groove rolling and drawing. After cold drawing, short specimens were heat treated at various temperatures from 550 to 800degC. During heat treatment, Mg reacted with a B(+SiC) layer forming a dense reacted layer inside an Fe sheath, which is composed of a MgB2 major phase and some minor impurity phases. Interestingly, the 7-core wire added with 5 mol% SiC heat treated at 600degC below the Mg melting point showed an apparent reaction forming a MgB2 layer and a fairly large amount of unreacted Mg inside a reacted MgB2 layer, suggesting that such formation is induced by solid-state reaction at the interface. On the other hand, almost all samples heat treated above 650degC showed MgB2 phase formation by typical liquid Mg infiltration producing a hollow at the center. The highest J c at 8 T and 4.2 K obtained for the multicore wire was 1.1 times 105 A/cm2 achieved by the addition of 5 mol% SiC and heat treatment at 600degC for 1 hr, which is slightly higher than the highest J c of the monocore wire (1.0 times 105 A/cm2) achieved for the wire added with 5 mol% SiC and heat treated at 670degC for 3 hr. The temperature of 600degC was lower than the melting point of Mg, suggesting that solid-solid reaction also forms a MgB2 layer in IMD. The small B layer thickness made it possible for Mg atoms to diffuse throughout the B layer at this low temperature.