Aussie last up about 0.1 pct at $1.0099, after climbing as high as $1.0135. Break above the 55-day MA at $1.0092 brings into view daily Ichimoku-cloud base around $1.0185.
NZ dollar last around $0.7909, after gaining 0.4 pct to $0.7935, its highest since early May. The kiwi may test $0.7988, the low on May 3, having already retraced more than 50 pct of its month-long decline in May.
Antipodeans also firmer on the yen, with Aussie up 0.2 pct at 80.03 and kiwi 0.5 pct higher at 62.66. Kiwi also outperforms the euro, which slips 0.3 pct to NZ$1.6035 .
But traders warn the relief rally may be short-lived as ongoing political uncertainty in Greece could fuel market volatility and trigger selling in the Aussie and the kiwi.
Political parties supporting Greece's international bailout will begin forging a government on Monday and still faces a monumental task of lifting the economy out of a deep recession.
Still, analysts say they expect to see demand for commodity currencies persist, particularly if speculation grows the US Federal Reserve may loosen monetary policy this week at its policy meeting.
Markets remain nervous about Europe, pricing in a 32 pct chance of a NZ rate cut next month, but economists expect the RBNZ to stay on the sidelines until next year.
Aussie interbank futures still have about 100 bps-worth of rate cuts factored in over the next 12 months.
Little market-moving data in Australia this week. Minutes of RBA's policy meeting on June 5, where it cut rates by 25bps, will be released on Tuesday.
In NZ, focus on Q1 current account and GDP data this week, with a Reuters poll forecasting a current account deficit of 4.6 pct of GDP and GDP growth of 0.5 pct.
Latest data shows NZ services sector activity edge up to its best level in six months in May, while forecasters chop NZ growth outlook in a NZIER survey. and
Aussie loses a bit of ground vs the kiwi, down 0.2 pct at NZ$1.2771.
Australian publisher Fairfax Media sells a 15 pct stake in popular NZ online trader Trade Me at A$2.70 a share, raising about A$160 mln.
NZ government bonds fall after the Greek vote, sending yields up to 13.5 bps higher.
Australian government bonds also pressured, with the three-year contract down 0.085 points at 97.630, while the 10-year contract sheds 0.065 points to 96.955.