* Yuan slides further, offshore rates fall to record lows
* Four U.S. rates in 2016 "in the ballpark" -Fed's Fischer
* Yen near three-month high vs dollar, nine-month high vs euro
* Aussie, kiwi sink more than 1 percent on China worries (Updates market action, changes dateline, previous LONDON)
By Richard Leong
NEW YORK, Jan 6 (Reuters) - The dollar held steady on Wednesday near one-month highs against a basket of currencies on the view of more U.S. interest rate hikes, while the yuan fell to its lowest since the 2010 opening of its offshore market on worries about the Chinese economy.
Further losses across global stock markets stoked bids for the low-risk Japanese yen, which hovered near a three-month high versus the greenback and a nine-month peak against the euro.
The yuan's depreciation "does look like it's contributing to the overall cautious market mood," said Eric Viloria, currency strategist at Wells Fargo (N:WFC) Securities in New York.
Despite market turbulence since the start of 2016 and data that signalled cooling in U.S. business activities, a top Federal Reserve official said the central bank remains on track for four more rate increases in 2016.
"My view is that those numbers are in the ballpark," Fed Vice Chairman Stanley Fischer told CNBC television. dollar index, which measures the greenback against a group of six currencies, .DXY was little changed at 99.448, a shade below the one-month peak set on Tuesday.
Sharp stock market losses in first three trading days of 2016 due to worries about the world's second-biggest economy unleashed a safehaven scramble for the yen.
"Everyone has been taken by surprise by the scale of the volatility this week. It's all driven by China," said Gian Marco Salcioli, head of FX sales at Italy's Intesa Sanpaolo (MI:ISP) Banca IMI (L:IMI) in Milan.
Adding to the mix were reports of a possible nuclear test in North Korea, helping push the yen higher against the dollar. greenback fell 0.4 percent to 118.58 yen JPY= , while the euro slipped 0.3 percent to 127.50 yen EURJPY= .
Investors were spooked by the rapid weakening of the Chinese currency, which fell almost 2.5 percent in just three days. That almost matched August's one-off devaluation, which touched off a global stock market selloff.
After the People's Bank of China again fixed its onshore rates for the yuan lower CNYFIX=SAEC , the less-regulated offshore rates for the currency fell more than 1 percent against the dollar to a record low of 6.7315 in London trade CNH=D3 .
The Australian and New Zealand dollars, among those most sensitive to Chinese growth and markets, have tumbled on the back of the weakening yuan.
The Aussie AUD=D4 was down 1.4 percent at $0.7065 after hitting its lowest in eight weeks, while the Kiwi NZD=D4 shed 1 percent at $0.6639 after touching its weakest in nearly a month.