They had less luck against a firm US dollar with the Aussie sluggish at $0.7826, not far from a three-week low of $0.7804 set on Monday. Support was found at a major retracement level of $0.7775.
It has shed more than 3 cents since it peaked above 81 cents earlier this month. Much of the slide is due to a broadly stronger US dollar on expectations of an interest rate hike later in the year by the Federal Reserve.
Even a bounce in iron ore prices has left Aussie dollar bulls cold. The mineral, Australia's top export earner, jumped 6 percent in three sessions.
The Antipodean currencies fared better against a wobbly euro which fell to A$1.3981, from Monday's peak of A$1.4077. The common currency has dropped 1.5 percent so far this month, largely due to renewed worries about Greece's finances. Support was found at A$1.3909.
The euro also touched a two-week trough of NZ$1.4945 , having slumped more than 4 cents in a week.
Against its US counterpart, the New Zealand dollar was stuck at $0.7310 and just above recent lows around $0.7284.
New Zealand data showed that an ongoing slide in exports of dairy products, the country's biggest earner, led to a widening in the annual trade deficit.
Investors are now waiting for co-operative Fonterra to release a forecast for farmgate dairy prices for the next 12 months.
Any improvement on this year's eight-year low payout of NZ$4.50 ($3.29) per kilogram for milk solids could boost demand for the kiwi in the near term.
New Zealand government bonds eased, nudging yields 1.5 basis points higher along the curve. Ten-year bond yields climbed to 3.82 percent, the highest since December.
Australian government bond futures were mixed, with the three-year bond contract off one tick at 97.930. The 10-year contract was up one tick to 97.0950.