The Australian share market has closed higher after federal Treasurer Josh Frydenberg delivered a budget update that showed a deficit that was not as high as the market had feared.

The benchmark S&P/ASX200 index finished up 19.4 points, or 0.32 per cent, at 6,094.5 points, while the All Ordinaries index gained 21.3 points, or 0.34 per cent, at 6,213.9.

The Australian dollar was trading at 71.52 US cents, down from 71.59 US cents at Wednesday’s close.