* Euro drops to 2-month low vs dollar, soft against yen
* Outlook fragile after euro's break below recent range
* Dollar index near 2-month high before U.S. election
LONDON, Nov 6 (Reuters) - The euro fell to a two-month low against the dollar on Tuesday, with the outlook for the single currency clouded by uncertainty over a parliamentary vote in Greece on budget and labour reforms.
Investors also headed for the safe-havens of the dollar and the yen with one eye on Tuesday's U.S. presidential election, which looked too close to call.
Opinion polls show Barack Obama and Republican challenger Mitt Romney in a dead heat, although the president has a slight advantage in several swing states.
The euro shed 0.2 percent to trade at $1.27635 on trading platform EBS, its lowest level in two months. That was well below its Sept. 17 high of $1.31729 struck after the European Central Bank pledged to buy government bonds of struggling euro zone countries.
The latest decline has pushed the euro out of the $1.2800/3200 trading range it has held since mid-September. Immediate support is seen around $1.2741, the 38.2 percent retracement of the euro's July to September rally.
``We are seeing investors getting disillusioned about the euro zone, the positive factor from the ECB's plan to buy bonds is fading and that is fundamentally weighing on the euro,'' said Neil Mellor, currency strategist at Bank of New York Mellon.
``There isn't much progress on when Spain will seek a bailout and now we have the Greek vote. Suffice to say if the vote fails, the euro will drop and the dollar will rally, but even if the vote passes, any rally in the euro will be short-lived.''
The parliament in Athens will approve or reject on Wednesday a government package of measures including cost cuts and tax hikes amounting 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 (in Athens) tomorrow,'' said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore.
EU Economic and Monetary Affairs Commissioner Olli Rehn said on Monday that Greece and its lenders are on track to reach a deal to unfreeze emergency payments at a meeting of euro zone finance ministers on Nov. 12.
A senior EU official earlier cast doubt on whether a deal could be struck next week.
DOLLAR UNDERPINNED
The dollar index rose to 80.811, not far from its two-month high of 80.843.
With the Republicans seen retaining control of the U.S. House of Representatives, a victory for Obama would be seen as raising the risk of policy paralysis over the country's 'fiscal cliff'.
If Congress cannot agree new arrangements, about $600 billion in government spending cuts and higher taxes will kick in early next year, all of which could hurt U.S. economic growth and underpin safe-haven assets.
The dollar underperformed the yen, however, falling 0.2 percent to 80.13 yen, and well below a six-month high of 80.68 yen hit on Friday. Traders said investors cut long dollar positions built up earlier.
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. The Australian dollar rose 0.5 percent to $1.0420.