By Sam Forgione

NEW YORK (Reuters) - The U.S. dollar hit its lowest level in nearly three weeks against the euro on Tuesday on U.S. political uncertainty, while the Mexican peso hit a more than three-week low on fears that Republican Donald Trump might win the U.S. presidential election.

Traders remained nervous about the outcome of the Nov. 8 election after news on Friday that the FBI was probing newly found emails related to U.S Democratic presidential candidate Hillary Clinton's use of a private server.

Clinton is viewed as the candidate of the status quo, while there is greater uncertainty over what a victory for Trump might mean for U.S. foreign policy, international trade deals and the domestic economy.

Analysts said a Trump victory could throw the Federal Reserve off its presumed course of hiking interest rates in December. Investors awaited Wednesday's Fed statement for any new indications that a rate increase is likely at the U.S. central bank's December meeting.

"The uncertainty over the election is certainly weighing on the dollar," said Stephen Casey, senior foreign exchange trader at Cambridge Global Payments in New York.

Analysts said traders who were bullish on the dollar were selling the currency ahead of the election. The selling accelerated in the afternoon session with a decline in U.S. shares, which put the benchmark S&P 500 <.SPX> stock index last down 0.88 percent.

The dollar index <.DXY>, which measures the greenback against a basket of six major rivals, fell about 0.8 percent to a nearly two-week low of 97.640. The index had gained 3.1 percent in October to mark its strongest month in just under a year.

The euro <EUR=> gained about 0.8 percent against the dollar to $1.1069, its highest since Oct. 12. The dollar fell 1.5 percent against the Swiss franc to a nearly one-month low of 0.9730 franc <CHF=> and fell about 1 percent against the yen <JPY=> to an eight-day low of 103.81 yen.

The Mexican peso <MXN=> fell about 2.2 percent against the greenback to 19.2700 pesos per dollar, its weakest level since Oct. 7.

A potential Trump victory has been viewed as a key risk for the Mexican currency given Trump's promises to clamp down on immigration and rethink trade relations.

"With dollar/Mex outperforming today, it highlights how markets are rethinking the election outcome and not ruling out a Trump presidency," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington, on the dollar's acceleration against the peso.

(Reporting by Sam Forgione; Editing by Meredith Mazzilli and David Gregorio)