The kiwi dollar was also up 0.5% to $0.6322, the strongest level in a month. It is eyeing April's top of $0.6383, after surging 1.7% last week.
Investors were bracing for a week where U.S. inflation data would test wagers that the next move in interest rates will be down, after the Federal Reserve dropped guidance about the need for future hikes last week.
Futures are 90% priced for steady rates in June and 38% for a cut as soon as July. That has weighed on the U.S. dollar, with it down 0.2% on Monday against a basket of major currencies. Tony Sycamore, market analyst at IG, said more battles are ahead for the Aussie dollar, even as it manages to stand above a key support level.
"If the AUD/USD were to see a sustained break above 0.6800/10, the recovery would extend towards 70 cents. Unfortunately, until then, it's business as usual, with more range trading expected between 0.6800 and 0.6570ish." On Tuesday, Australia will unveil a huge turnaround in its budget bottom line under the centre-left Labor government.
There is a good chance that Australia will forecast a small budget surplus, the first in 15 years, although analysts expect a muted market reaction to it.
"Enough details have been revealed to limit the chances of any noticeable impact on FX markets, but the expected improved budget bottom line relative to the October update should look positive in the global context," said Sean Callow, senior currency strategist at Westpac.
Australian bonds slid a little, tracking U.S. counterparts.
Three-year bond yields rose 10 basis points at
3.085%, while ten-years were 7 bps higher at 3.407%.
(Reporting by Stella Qiu; Editing by Sonali Paul)