* Euro dangles near 2-month low vs dollar
* Outlook fragile after euro's break below recent range
* Aussie dollar awaits RBA rate decision due 0330 GMT
SINGAPORE/SYDNEY, 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 a tight U.S. presidential race, although President Barack Obama has a slight lead in the eight or nine battleground states.
The euro eased 0.1 percent to $1.2786, 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 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.
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.
``I think the market ought to be focusing more on the imminent situation facing Greece, even more than the U.S. presidential election,'' said Daisuke Karakama, market economist for Mizuho Corporate Bank in Tokyo.
The issue of when international lenders will sign off on the new aid tranche for Greece is likely to be a focal point for the market this month, Karakama added.
A senior EU official said on Monday that a deal to keep near-bankrupt Greece afloat by providing more bailout money is unlikely to be struck next week when euro zone finance ministers meet in Brussels.
``A deal is still likely in November, but not necessarily on November 12,'' the official said.
Until now, next Monday's Eurogroup meeting had been pencilled in as a likely venue to sign off on a new Greek programme.
RBA RATE DECISION
The Australian dollar held steady at $1.0369.
Key for the Aussie is the Reserve Bank of Australia's (RBA) interest rate decision due at 0330 GMT. Analysts polled by Reuters mostly expect a quarter-point cut, but markets are more circumspect, giving only a 50-50 chance.
``While it looks like it will be a tight decision, we continue to expect another 25-basis-point cut,'' strategists at Westpac Bank said.
They added that a rate cut should see the Aussie return to a $1.02-handle, while a steady RBA would open up a run at $1.0475.
A cut will take the cash rate to 3.0 percent, matching a record low seen during the global financial crisis.
The U.S. dollar eased 0.1 percent to 80.23 yen. The greenback had rallied to a six-month high of 80.68 yen on Friday after data showed the U.S. economy created more jobs than expected last month.