[en] Helical windings of Fe-sheathed MgB₂ wires with different dimensions were fabricated by a wind-and-react process. Wires with a cross-sectional area of 1 mm² and 20% superconductor core were made using the powder-in-tube (PIT) method and ultra-fine starting precursors. Very good grain connectivity as well as high core density was obtained by using this method. At 20 K and self-field, the critical current of a coil with an ID of 12 mm and 12 turns was 360 A, which is equivalent to a J_c of 1.8 x 10⁵ A cm^-2. At a 6 T external magnetic field and 4.2 K, a coil with an ID of 140 mm and 10 turns possessed a J_c of 1 x 10⁴ A cm^-2. These results are a step towards the application of MgB₂ wires in the temperature range of 20-30 K and high magnetic fields