The Australian share market has enjoyed its best day in seven weeks, rallying alongside its peers in Asia amid optimism over a gradually reopening world economy.

The S&P/ASX200 benchmark index closed on the highs of the day on Tuesday up 164.4 points, 2.93 per cent, at 5,780 points, while the All Ordinaries index was up 160 points, or 2.79 per cent higher, at 5,889.9.

The Australian dollar was buying 65.80 US cents, up from 65.24 US cents at the close of trade on Friday.