Polls indicate the election between President Barack Obama and Republican challenger Mitt Romney will be extremely close and the risk of a change in policy in the world's largest economy was keeping investors on the sidelines.

"With the uncertainty over the U.S. election and Greece it is likely that investors will be sitting on their hands again today," said Heinz-Gerd Sonnenschein at German bank Postbank

The MSCI index of world stocks was steady at 329.88 points as European markets opened.

London's FTSE 100, Frankfurt's DAX and the Paris CAC-40 were between flat and up 0.2 percent after falls on Monday. The FTSEurofirst index of top European shares was up 0.1 percent at 8.10 a.m. EDT.

The euro traded near a two-month low of $1.2785, versus the dollar, with its outlook clouded by uncertainty over a Greek parliamentary vote on Wednesday on austerity steps needed for Athens to secure international aid.

There is also plenty of European data on Tuesday, including final euro zone PMI October readings and German industrial figures.

In bond markets, German government Bund futures were steady at 142.11, having rallied on Monday.

Risk-aversion also kept the dollar near a two-month high against a basket of major currencies and most asset markets were trading in tight ranges. Oil and gold were both barely changed.

In Asian trading, Japan's Nikkei stock market fell 0.4 percent. Australian shares rose 0.2 percent after the country's central bank surprised by keeping rates on hold, helping to lift the MSCI index of Asia-Pacific shares outside Japan 0.4 percent.

(Reporting by Marc Jones; editing by Anna Willard)

• A Permanent Economic Emergency