The Australian dollar is up sharply against its US counterpart amid a slight rebound in risk appetite following US President Donald Trump's firing of controversial adviser Steve Bannon.

At 0635 AEST on Monday, the Australian dollar was worth 79.20 US cents, up from 78.96 US cents on Friday.

Westpac's Imre Speizer said the US dollar had moved sideways during Friday's session before closing lower.

"The US dollar index ranged sideways and closed the day down 0.2 per cent ... [while the] AUD rose from 0.7980 to 0.7944.," he said in a Monday morning note.