We report results of the first phase of observations with the Australia Telescope Compact Array ( ATCA ) at 5 and 9 GHz of the fields around 411 \gamma -ray sources with declinations < +10 \degr detected by Fermi but marked as unassociated in the 2FGL catalogue .
We have detected 424 sources with flux densities in a range of 2 mJy to 6 Jy that lie within the 99 per cent localisation uncertainty of 283 \gamma -ray sources .
Of these , 146 objects were detected in both the 5 and 9 GHz bands .
We found 84 sources in our sample with a spectral index flatter than -0.5 .
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 where available .