* Euro hits eight-week lows vs USD, five-week lows vs AUD
* EUR/USD breaks out of range, outlook fragile
* Aussie dollar awaits RBA rate decision due 0330 GMT
SYDNEY, Nov 6 (Reuters) - The euro languished at eight-week lows versus the greenback on Tuesday, having fallen broadly as a Greek parliament vote on a new austerity package loomed.
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 single currency was at $1.2790, having fallen as far as $1.2767 following a break of the Oct. 1 trough around $1.2804.
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 July-Sept rally.
Strategists at Societe General said uncertainty about the Greek parliament vote may be enough for EUR/USD to reach the $1.2741 retracement level, before the usual short-USD/long-EM demand weakens the momentum.
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.
The euro struggled at one-week lows versus the yen at 102.70 and wallowed at a five-week trough on the Australian dollar at A$1.2339.
Against the dollar, the Aussie fetched $1.0363, having retraced about half of Friday's 0.6 percent slide from $1.0418 to $1.0325.
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.
Dollar/yen also had a directionless session on Monday, with the greenback retracing most of Friday's rally to a six-month high of 80.68. It last stood at 80.30.