The Australia and the New Zealand dollars strengthened against their major currencies in the Asian session on Wednesday, as oil prices rebounded after the release of API crude oil inventories data overnight.

Crude oil for August delivery are currently up $0.13 at $61.14 a barrel.

Industry group American Petroleum Institute said late Tuesday that U.S. crude stockpiles were estimated to have fallen by 3.2-million-barrel last week.

Traders are also likely to keep a close eye on the official U.S. inventories report from the Energy Information Administration, due later in the day. Analysts expect crude oil inventories to have fallen for an eighth week.

Meanwhile, Asian shares traded higher, as investors optimistically wait for a Greek debt deal.

Analysts say that Greece's latest proposals go much further than expected but cautioned that substantial challenges remain, with Greek parliamentary approval for the proposals seen as a key risk. Nevertheless, the developments in negotiations between Greece and its creditors have stymied talk of default for now.

In other economic news, data from the Conference Board showed that a leading index for the Chinese economy spiked in May, rising 1.1 percent. That follows the upwardly revised 1.4 percent jump in April and the 0.2 percent increase in March.

Tuesday, the Australia and New Zealand dollars showed mixed trading against the its major rivals. While the Australia and the NZ dollars fell against the U.S. dollar and the yen, they rose against the euro. Meanwhile, the Australian dollar fell against the Canadian dollar too.

In the Asian trading today, the Australian dollar rose to a 3-week high of 1.4403 against the euro, from yesterday's closing value of 1.4431. If the aussie extends its uptrend, it is likely to find resistance around the 1.39 area.

Against the Canadian dollar, the yen and the U.S. dollar, the aussie advanced to a 6-day high of 0.9556, a 5-day high of 96.03 and a 2-day high of 0.7757 from yesterday's closing quotes of 0.9533, 95.85 and 0.7733, respectively. The aussie is likely to find resistance around 0.97 against the loonie, 97.50 against the yen and 0.80 against the greenback.

The NZ dollar also rose to a 6-day high of 1.6258 against the euro and a 2-day high of 85.06 against the yen in the Asian trading today, from yesterday's closing quotes of 1.6278 and 84.90, respectively. If the kiwi extends its uptrend, it is likely to find resistance around 1.58 against the euro and 87.00 against the greenback.

The kiwi edged up to 0.6873 against the U.S. dollar, from yesterday's closing value of 0.6849. On the upside, 0.70 is seen as the next resistance level for the kiwi.

Looking ahead, Swiss UBS consumption indicator for May is due to be released at 2:00 am ET.

German Ifo business climate index for June and U.K. BBA mortgage approvals for May are also slated for release in the European session.

In the New York session, third estimate of U.S. GDP for the first quarter is set to be announced.

At 7:00 am ET, Eurozone finance ministers meet for last-ditch talks in Brussels to hammer out a loans-for-reforms deal with Greece without which Athens will default on June 30 on its repayment to the IMF in Brussels.

Three hours later, European Central Bank Vice-President Vitor Constancio will participate in a Symposium on 'Debt - Economic, Political and Moral Consequences' organised by the House of Finance (SAFE) of Goethe University in Frankfurt.

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