SYDNEY (Reuters) - The euro struggled to gain any momentum in early Asian trade on Tuesday, while the Australian dollar nursed losses as bears bet on the prospect of a cut in interest rates later in the session.

The common currency was at $1.3073, having pulled back from Monday's high of $1.3141. It fell as far as $1.3053 after the head of the European Central Bank (ECB) reiterated the central bank's readiness to cut interest rates again if needed.

In a speech in Rome, ECB President Mario Draghi said the bank would monitor incoming data closely and be ready to cut rates further, including the deposit rate currently at zero.

Initial support for the euro is seen around $1.3024, the 76.4 percent retracement of its April 24-May 1 rally and the 55-day moving average at $1.3021.

Vassili Serebriakov, strategist at BNP Paribas, said further downside risks for the euro are likely to be limited thanks to ongoing significant support from European market sentiment.

"Both European financial equities and the core-periphery spreads have been moving in a favorable direction and indicate that EUR/USD can potentially strengthen to the 1.34-1.35 area."

Trading was relatively subdued overnight with UK financial markets closed for a bank holiday. Japanese markets reopen on Tuesday after a four-day long weekend.

The common currency also ceded a bit of ground against the yen, slipping to 129.85 from Monday's session high of 130.40. However, it remained near a 3-year high of 131.10 set last month.

The pullback in the euro saw the dollar index drift up to 82.340 .DXY from Monday's low of 81.982, helping keep it well away from last week's 2-month trough of 81.331.

Against the yen, the greenback was at 99.35, having risen on the back of upbeat U.S. jobs data last Friday. It appeared to be gearing up for another go at tough resistance at the psychological 100 level.

The big mover overnight was the Australian dollar, which fell 0.6 percent to $1.0253 as markets positioned for a possible interest rate cut by the Reserve Bank of Australia (RBA).

While the majority of analysts polled by Reuters suspect the RBA will not cut, markets have priced in a 50-50 chance of a quarter point easing in the cash rate to a record low 2.75 percent.

Those arguing for a cut point to still tame inflation at home and recent signs of slower growth in China, the country's biggest export market.

Others, however, say the bank will wait for employment data later this week and a report on company investment plans later in the month before making a decision.

Should the RBA hold steady at 0430 GMT, the Aussie should squeeze higher to test resistance in $1.0300/23 zone. Strong support is seen at the overnight low near $1.0220, a level which has propped the currency up in the past few weeks.

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