The Australian share market notched small gains on Thursday, with banks and AGL helping the advance, as investors managed to hold on to early optimism generated by US tax cut plans.

The S&P/ASX 200 index ended the day up 6 points, or 0.1 per cent, at 5670.40, for its first advance in three sessions. Investors showed a marked lack of conviction earlier in the week, wiping out early gains by the end of the trading day.

US markets provided an optimistic base for Thursday's ASX session, with shares advancing on Wall Street after US president Donald Trump outlined his plans to reform the US tax system.

RBC analysts said that if Mr Trump's tax cut plan was passed in its current form "and acknowledging that some key details are still missing," a good baseline would be that the tax plan could increase US GDP growth by at least 0.5 per cent per year.