* Downbeat data add ECB easing expectations * Trading light ahead of Fourth of July holiday in U.S. * Aussie steady; RBA leaves rates on hold NEW YORK, July 3 (Reuters) - The euro fell against the dollar o n Tuesday with investors betting that the European Central Bank will cut its benchmark interest rate at its meeting on Th ursday amid poor euro zone data and doubts about a European plan to support indebted countries. Signs out of the euro zone were generally discouraging, keeping sentiment toward the euro bearish. The jobless rate rose to a record in May and factory activity contracted again in June. That overshadowed any optimism remaining from an announcement last week that euro zone leaders agreed rescue funds could be used to stabilize bond markets without forcing countries that comply with EU budget rules to adopt extra austerity measures or economic reforms. Finland and the Netherlands, two of the currency bloc's most hard-line creditor states, had already cast doubt on the measures on M onday. "This week's key event for the euro remains the ECB meeting on Thursday, where expectations are for a 25 basis point cut in the policy rate to 0.75 percent," said Eric Theoret, currency strategist at Scotiabank in Toronto. "While a rate cut had been discussed at the last meeting, a majority of the governing council had voted to maintain rates. It has since been rumored that a majority now favors easing rates." The euro was last down 0.2 percent at $1.2566, just off the session low of $1.2558 and well below a peak of $1.2693 hit on Friday in the wake of an EU summit agreement, the latest attempt to stem the ongoing crisis. Against the safe-haven yen the euro was up 0.2 percent at 100.21 yen, still well below post-summit highs above 101.00 yen. Activity was relatively light, which may have been exacerbating moves, ahead of the Fourth of July U.S. holiday, traders said. ECB AWAITED Many traders expect the ECB to move on Thursday to bolster the euro zone economy by cutting its main refinancing rate. Jaco Rouw, fund manager at ING Investment Management in London, said there were differing opinions as to the impact of any rate cut, but he expected the euro to weaken given the poor economic outlook for the currency bloc. "One opinion is that the rate cut might boost risk sentiment and reduce the risk premium in the euro which could be positive, but a lower rate in itself would be euro negative," he said. "In the longer term, based on economic developments, there is still room for more monetary easing in Europe so we would position for a weaker euro." Some also expect the Federal Reserve to announce a third round of asset purchases, dubbed QE3, perhaps as soon as the U.S. central bank's next policy meeting from July 31 to Aug. 1. Australia's central bank held its main cash rate steady at 3.5 percent on Tuesday, to continue to gauge the effect of back-to-back cuts. The Australian dollar was little changed at $1.0243, still within half a cent an earlier two-month high. The U.S. dollar rose 0.4 percent and bought 79.80 yen . Traders said dollar buying by model funds was offset by selling by Asian retail accounts.

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