We report results of the first phase of observations with Australia Telescope Compact Array (ATCA) at 5 and 9GHz of the fields around 411 {gamma}-ray sources with declinations less than +10{deg} detected with Fermi but marked as unassociated in the 2FGL catalogue. We have detected 424 sources with flux densities in a range of 2mJy to 6Jy in the fields of 283 {gamma}-ray sources within their position error ellipses drawn to cover the area of 99 per cent probability of their localisation. Of them, 146 objects were detected in both bands. We found 84 sources with spectral index flatter than -0.5 in our sample. The majority of detected sources are weaker than 100 mJy and for this reason were not found in previous surveys. Approximately 1/3 of our sample, 128 objects, have the probability of being associated by more than 10 times than the probability of being a background source found in the vicinity of a {gamma}-ray object by chance. We present the catalogue of positions of these sources, estimates of their flux densities and spectral indices when available.