* U.S., European shares fall on investor caution
* Dollar index touches 2-month highs on safety bids
* U.S. presidential race stays tight before Tuesday vote
* Eyes also on Chinese leadership, euro zone debt crisis
NEW YORK, Nov 5 (Reuters) - World stocks fell and the dollar edged up on Monday as investors played it safe before Americans choose their president and Greece headed into two key votes to secure further rescue funds.
Some investors see the U.S. election as a hurdle to get through so markets can turn attention to the "fiscal cliff" budget battle. The world's biggest economy faces the possibility of $600 billion in automatic spending cuts and tax hikes should Congress not reach a deal to mitigate its effects.
"People are pausing ahead of the election and what that means for the fiscal cliff," said Jim Paulsen, chief investment officer at Wells Capital Management in Minneapolis.
Opinion polls show the race between President Barack Obama and Republican challenger Mitt Romney remains neck-and-neck at the start of the last day of campaigning, and the uncertainty over the outcome left financial markets jittery.
There is a possibility that the election will be too close to call in a number of states. A delayed result could roil markets as it did in the protracted 2000 election battle.
Delegates at a G20 meeting this weekend in Mexico City pressed the United States to act decisively on tax and spending issues.
Safe-haven bids pushed the U.S. dollar up about 0.2 percent to two-month highs against a basket of major currencies and German two-year government bond yields dropped below zero for the first time in two months on safety demand.
Demand for low-risk assets pushed the prices on benchmark U.S. 10-year Treasury notes up 10/32 with a yield of 1.6823 percent, down 3.5 basis points from late on Friday.
The Dow Jones industrial average was down 13.15 points, or 0.10 percent, at 13,080.01. The Standard & Poor's 500 Index was down 1.23 points, or 0.09 percent, at 1,412.97. The Nasdaq Composite Index was up 5.79 points, or 0.19 percent, at 2,987.92.
European shares were provisionally closed 0.56 percent lower after ending the previous week at a two-week high.
The MSCI world shares index was 0.35 percent lower as Tokyo's Nikkei index closed 0.5 percent weaker following Friday's Wall Street sell-off.
In commodity markets, Brent crude oil turned higher, erasing early losses. December Brent futures last traded up 35 cents at $106.03 a barrel after they being bogged down earlier by a strong dollar and a drop in demand in the wake of Sandy, the deadly storm that pummeled the U.S. Northeast a week ago.
Sandy disrupted the distribution of gasoline and left millions without power in the region.
In line with the broader market caution, gold gained about 0.3 percent at $1,682.05 an ounce after Friday's 2 percent plunge.
BEYOND U.S. ELECTION
While monitoring on the outcome of the tight race for the White House, investors were mindful of the leadership transition in China and the votes by Greece to secure fresh rescue funds.
It was expected that Greek Prime Minister Antonis Samaras' coalition will muster enough support on Wednesday to win a vote on structural reforms and a follow-up vote on Sunday on an austerity budget for 2013.
These fiscal reforms are critical for the debt-laden nation to receive more financial aid from lenders from an International Monetary Fund and European Union bailout that has been on hold since the summer.
"Without the additional funds, the country would be put back on the path toward an exit from the euro," said Karl Schamotta, senior strategist at Western Union Business Solutions in Calgary.
On Thursday, China's ruling Communist party will begin the 18th congress in its history with the culmination a week later in the expected selection of Xi Jinping to succeed President Hu Jintao.