The Australian share market has given up its early gains to close lower, despite gold prices surging to a fresh all-time high and coming close to the breaking $US2,000 an ounce.

The benchmark S&P/ASX200 index finished Tuesday down 23.7 points, or 0.39 per cent, at 6,020.5 points, while the All Ordinaries index finished down 22.8 points, or 0.37 per cent, at 6,146.8.

The Australian dollar meanwhile was buying 71.32 US cents, unchanged from Monday’s close.