AUD/USD hit 1.0601 during late Asian trade, the pair's highest since March 20; the pair subsequently consolidated at 1.0574, inching up 0.05%.
The pair was likely to find near-term support at 1.0535, Monday's low and resistance at 1.0636, the high of March 19.
The RBA left its benchmark interest rate unchanged at 3.5%, in a widely expected decision.
The Australian dollar has strengthened against the U.S. dollar since the RBA's last rate cut in early June.
In its policy statement, the RBA said the exchange rate "has remained high, despite the observed decline in the terms of trade and the weaker global outlook."
Overall market sentiment continued to be supported by expectations that the European Central Bank will soon act to cut Spanish and Italian borrowing costs.
The Aussie was higher against the euro, with EUR/AUD slipping 0.17% to 1.1713.
Later in the day, U.S. Federal Reserve Chairman Ben Bernanke was to speak at an event in Washington DC.