* Dollar hit after some polls show Trump leading Clinton
* Greenback hovers near 3-week low vs euro, 12-day low vs yen
* Mexican peso at its weakest in a month vs dollar
* Fed awaited, but politics seen overshadowing fundamentals (Updates prices, adds details and quotes)
By Shinichi Saoshiro
TOKYO, Nov 2 (Reuters) - The dollar slumped on Wednesday as the U.S. presidential election increasingly looked too close to call, jangling investors' nerves and fuelling demand for perceived havens such as the Japanese yen.
The greenback fell to a three-week low against the euro and a 12-day low versus the yen, as some polls showed Republican Donald Trump inching ahead after the FBI said on Friday it was probing newly-found emails related to Democrat Hillary Clinton's use of a private server.
The euro was up 0.1 percent at $1.1065 EUR= , near the peak of $1.1069 seen the previous day, its highest since Oct. 11.
The dollar extended overnight losses and was down 0.4 percent at 103.700 yen JPY= after seeing a 12-day trough of 103.650. It has skidded from a three-month peak of 105.540 reached last week.
The safe-haven yen benefited as a risk-averse mood set in and weakened equities across Asia. Tokyo's Nikkei .N225 slid more than 1 percent.
"The dollar could retake the 105 yen threshold on a Clinton win. Meanwhile 'Trump risk' cannot be ruled out, so I see the pair stuck at current levels for the next week," said Koji Fukaya, president at FPG Securities in Tokyo.
"Even a strong U.S. non-farm payrolls report (on Friday) may not be able to lift dollar very much, the risk of it sliding on a weak report is probably greater."
With less than a week to go until the Nov. 8 U.S. elections, politics have overshadowed fundamentals, with a Federal Reserve policy decision due late on Wednesday possibly relegated to a sideshow.
The Fed is expected to keep interest rates unchanged but set the stage for a hike in December amid signs the economy is picking up steam.
"The currency market is unlikely to treat the Fed meeting as a strong factor," said Shin Kadota, chief Japan FX strategist at Barclays (LON:BARC) in Tokyo. "The Fed has been hinting of a December rate hike for a while, and the market is focused on events related to the U.S. elections."
"While Clinton may still hold a lead over Trump, the dollar could suffer another round of declines if new polls show Trump catching up."
Clinton held a 5 percentage-point lead over Trump, according to a Reuters/Ipsos opinion poll released on Monday, little changed since the FBI announcement.
But a poll by ABC News showed Trump leading by 1 point and the Los Angeles Times put the Republican more than 2 points ahead.
The Mexican peso, considered a rough barometer of the ebb and flow of Trump's fortunes in the presidential race, struggled at a near one-month low against the greenback.
The Mexican currency retreated to as low as 19.317 pesos per dollar MXN= , its weakest since Oct. 7.
A potential Trump victory has been viewed as a key risk for the Mexican currency, given the candidate's promises to clamp down on immigration and rethink trade relations.
The Australian dollar, sensitive to shifts in risk appetite, was down 0.4 percent at $0.7624 AUD=D4 .
The Aussie handed back most of the gains it made the previous day after the Reserve Bank of Australia left rates steady and refrained from including an explicit easing bias in its statement.
The New Zealand dollar touched a two-week high of $0.7225 NZD=D4 after the country's jobless rate dropped to near eight-year lows last quarter, fuelling speculation the central bank's easing cycle may be almost done.
The dollar index .DXY was little changed at 97.672, hovering just above a two-week trough of 97.640 plumbed the previous day. (Editing by Richard Borsuk and Kim Coghill)