Shares on the Australian market have closed higher amid a broad based rally in Asian markets.

The benchmark S&P/ASX200 index closed up 35.5 points, or 0.53 per cent, at 6700.30 on Tuesday.

The index rose as high as 6725 in the first 10 minutes of trading but lost ground later in the session amid lower trading volumes after the Christmas break.

The All Ordinaries closed up 44.6 points, or 0.64 per cent, to 6962.10.

Shares across Asian markets rose as hopes of a global economic recovery improved after US President Donald Trump on Sunday signed a $US2.3 ($A3.0) trillion pandemic support bill and the UK and European Union managed to stitch together a last minute Brexit deal.

The Aussie dollar was buying 75.95 US cents at 1615 AEDT, higher from 75.81 US cents at Thursday’s close.