* German industrial orders data pushes euro higher * Gains seen temporary as ECB ready to lower rates * Australian dollar drops after RBA cuts cash rate By Gertrude Chavez-Dreyfuss NEW YORK, May 7 (Reuters) - The euro firmed across the board on Tuesday after data showing German industrial orders beat forecasts but expectations the European Central Bank could ease monetary policy further could limit its gains. The Reserve Bank of Australia, meanwhile, stunned the market earlier in the global session by cutting interest rates to a record low, undermining the Australian dollar, which fell to its weakest level in two months versus the U.S. currency. The euro hit a session high of $1.3131 in the wake of the German economic data and by early morning trading was up 0.3 percent at $1.3108. Industrial orders for March rose 2.2 percent from February, beating a forecast of a 0.5 percent drop and providing some relief to the single currency. "The data offered a hopeful sign for recovery, which lent mild support to the euro," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington. "Still, the general outlook for the region is decidedly less auspicious, particularly after ECB President (Mario) Draghi on Monday again stated that bank officials were on data watch and persistent weakness in the core would offer scope for another rate cut." But Camilla Sutton, chief currency strategist at Scotiabank in Toronto, believes the euro is better supported than the dollar in the near term because the European Central Bank is not engaged in the type of aggressive monetary stimulus the Federal Reserve has undertaken. "The truth is relative monetary policy still favors the ECB in terms of currency strength," Sutton said. "As long as ECB is not engaged in any balance sheet expansion, that's currency-positive and even if there's a risk of lower rates, the interest rate differential between the euro and the dollar is so close, it's not even material." She thinks the euro could hold that $1.30 level over the next few weeks. In the options market, one-month implied volatilities were near their lowest since January, indicating the euro was likely to stay in a range against the dollar. The euro has been trading between $1.2740 and $1.3243 since March. 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. Traders also cited bids from Asian sovereign accounts at sub-$1.3050 levels. The euro regained ground against the yen, up 0.2 percent at 130.05 yen but still some way off a three-year high of 131.13 set last month. The dollar was flat against the Japanese currency at 99.20 yen, with traders citing interest from some hedge funds to buy the greenback. AUSSIE HURT The Australian dollar hit a two-month trough of US$1.0152 after the central bank slashed rates to a record low of 2.75 percent. The market had been divided on the chances of a cut, but prospects of further loosening could weigh on the currency. The growth-linked Aussie dollar was last at US$1.0162, down 0.9 percent on the day. RBA Governor Glenn Stevens made particular mention of the exchange rate, stating that the Aussie dollar, "has been little changed at a historically high level over the past 18 months, which is unusual given the decline in export prices and interest rates during that time." Boris Schlossberg, managing director of FX Strategy at BK Asset Management in New York said Stevens' remarks were a "clear signal by the central bank that it would like to see the (AUD/USD) pair trade lower - at least below parity - in order to rebalance the economy and stimulate the export sector."