TOKYO (Reuters) - Asian shares and the dollar steadied on Tuesday with investors' risk appetite curbed by uncertainty over the outcome of the tight U.S. presidential election and renewed doubts over Greece's political ability to push through severe fiscal reforms.

Risk-aversion underpinned the dollar near a two-month high against a basket of major currencies of 80.843 hit on Monday, while pressing the euro down 0.1 percent to $1.2782, near Monday's two-month low of $1.2767.