We describe an effective, versatile technique for reconstructing the electric conductivity distribution from magnetic vector field measurements. Using magnetic vector field data measured over a region of interest (ROI), the assumed steady current vector field is reconstructed to perform conductivity reconstruction. As the current sources/current flow outside the ROI significantly contribute to magnetic fields over the neighbourhood of the ROI border, the extra contributions are reduced in the measured magnetic field data using a derived spatial weight function. The remaining magnetic field measurement errors are coped with utilizing a mollification method in conjunction with a regularization method. In a straightforward manner, our current field reconstruction technique is combined with our previously reported conductivity reconstruction technique. The combined non-contact conductivity reconstruction technique in principle allows handling of an arbitrary geometry of the target conductive ROI and arbitrary current sources existing outside the ROI. The technique is particularly effective when an inherent current flow exists and only field measurements are needed. Technique feasibility is simply verified by reconstructing a 2D conductivity distribution using simulated, noise-filled, magnetic field data. Resultant reconstructions indicate the technique to be a practical means for robustly reconstructing target conductivity distributions.