* Euro comes off two-month low vs dollar, soft against Aussie
* U.S. election results could impact 'fiscal cliff' talks
* Greek parliament to vote on austerity reforms
NEW YORK, Nov 6 (Reuters) - The U.S. dollar edged lower against major currencies on Tuesday as investors booked profits on recent gains, with trading subdued ahead of the results of the U.S. presidential election.
The euro hit a two-month low against the dollar before recovering to trade slightly higher as investors awaited a parliamentary vote in Greece on the country's austerity reforms needed to secure international aid.
Opinion polls showed incumbent Barack Obama and Republican challenger Mitt Romney in a dead heat, although the president has a slight advantage in several swing states.
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 so-called`` 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. Ironically, these worries have boosted the dollar, which is seen as a safe-haven, in recent days.
``For FX in the near-term the key driver is the 'fiscal cliff'; however, in the medium term it is the ability to craft a credible fiscal plan, the growth outlook and who is likely to lead the Fed in January 2014,'' said Camilla Sutton, chief currency strategist at Scotia Capital in Toronto.
The dollar index, which tracks the value of the greenback against a basket of major currencies, slipped 0.2 percent to 80.623, but still remains close to a two-month high of 80.843 set on Monday.
The euro rose 0.1 percent to $1.2810 after having dropped to $1.2761 on Reuters data, its lowest level in two months.
That was well below its Sept. 17 high of $1.3169 struck after the European Central Bank pledged to buy government bonds of struggling euro zone countries that requested help.
Immediate support is seen around $1.2736, the 38.2 percent retracement of the euro's July to September rally.
Greek workers begin a 48-hour strike on Tuesday to protest against a new round of austerity cuts that unions say will devastate the poor and drive a failing economy to collapse.
Athens, however, needs parliamentary approval for the package, which includes slashing pensions by as much as a quarter for some and scrapping holiday bonuses, to ensure its European Union and International Monetary Fund lenders release more than 31 billion euros ($40 billion) of aid, much of it aimed at shoring up banks.
``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 it 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.''
Traders said investors were adding to short positions against the euro and looking to sell at higher levels after weak euro zone PMI data bore grim tidings for the fourth quarter and German industrial orders slumped in September.
The euro fell to a two-month low against the high-yielding Australian dollar at A$1.2236, while it plumbed a one-month low against the British pound.
The dollar was little changed at 80.26 yen, and well below a six-month high of 80.67 yen hit on Friday.
The Australian dollar climbed after Australia's central bank decided against a rate cut and kept its benchmark rate at 3.25 percent, citing higher 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 0.7 percent to a near six-week high of $1.0445.