* Aussie surges after RBA keeps interest rates steady
* Euro dangles near 2-month low vs dollar
* Outlook fragile after euro's break below recent range
SINGAPORE, Nov 6 (Reuters) - The euro languished near a two-month low versus the dollar on Tuesday, with its outlook clouded by uncertainty over a Greek parliamentary vote on austerity steps needed for Athens to secure international aid.
Traders said the market was also in a wait-and-see mode ahead of Tuesday's U.S. presidential election.
National opinion polls show President Barack Obama and Republican challenger Mitt Romney in a virtual dead heat, although Obama has a slight advantage in several vital swing states.
The euro eased 0.1 percent to $1.2788, staying near the previous day's low of $1.2767 set on trading platform EBS, the single currency's lowest level in about two months.
The latest decline has pushed the euro out of the $1.2800/3200 trading range held since mid-September. Immediate support is seen around $1.2741, a level representing the 38.2 percent retracement of the euro's July to September rally.
The Greek parliament will decide to approve or reject on Wednesday the government's package of measures including cost cuts and tax hikes that should amount to 13.5 billion euros ($17 billion) by 2016.
Approval of the reforms and the passage of the 2013 budget are crucial to unlocking 31.5 billion euros in aid from an IMF and EU bailout that has been on hold for months.
``Everyone is nervous because of all the uncertainty over what might happen tomorrow,'' said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore, referring to the looming parliamentary vote in Greece.
Still, EU Economic and Monetary Affairs Commissioner Olli Rehn said on Monday that international lenders and Greece are on track to reach a deal to unfreeze emergency lending to Athens at a meeting of euro zone finance ministers on Nov. 12.
A senior EU official, speaking on condition of anonymity, had earlier cast doubt on whether a deal on Greece could be struck next week. But Rehn said a deal would be struck next Monday, when euro zone ministers, called the Eurogroup, meet in Brussels.
RBA STANDS PAT
The Australian dollar climbed after Australia's central bank kept interest rates unchanged at 3.25 percent, citing higher domestic inflation and an improved global background, although it still left the door open to more stimulus if needed.
The decision came as a surprise to some market players who had been expecting the Reserve Bank of Australia (RBA) to lower interest rates.
The Australian dollar rose 0.6 percent on the day to $1.0428 .
Roy Teo, FX strategist for ABN AMRO Bank in Singapore, said the Australian dollar's gains may be limited going into the year-end, especially since Australia's central bank could lower interest rates next month.
``We still believe that the RBA is on an easing cycle,'' Teo said.
The U.S. dollar fell 0.3 percent versus the yen to 80.03 yen , pulling away from a six-month high of 80.68 yen hit on Friday. Traders said the dollar came under pressure against the yen due to position squaring.