* Dollar up broadly as investors back away from risk
* Sterling tumbles as break of $1.6000 triggers stops
* Fed Governor Warsh talks of eventual policy normalisation
* Most Asian stocks track Wall St lower
By Satomi Noguchi
TOKYO, Sept 25 (Reuters) - The dollar rallied broadly on Friday as short-covering gathered pace a day after major central banks jointly announced steps to scale back massive injections of the U.S. currency.
Sterling tumbled further to a four-month low against the dollar as a break of major support levels triggered a wave of stop-loss sales.
The rush towards risky assets such as higher-yielding currencies was first halted by Thursday's weak U.S. home sales figures, which overshadowed a drop in weekly jobless claims.
Then dollar selling slammed into reverse when the Federal Reserve, and a gaggle of central banks, announced they were paring back injections of dollar liquidity.
Analysts noted that demand at those dollar auctions had already waned, so scaling back the operations was actually a sign that credit conditions were easing.
"Nevertheless, markets are fragile at the moment and there was a visible announcement effect -- markets afraid that as liquidity is mopped up, then some risk appetite may go with it," said Adam Carr, senior economist at ICAP Australia.
The dollar index was up 0.1 percent at 76.947, after rising over 1 percent on Thursday. That was the third time in two weeks the index had bounced from 76.00, making dealers cautious about shorting the currency any further.
Instead, talk now was of the need for a sizable correction, perhaps back to 78.0, before the downtrend could resume.
Hideaki Amikura, deputy general manager of the forex division at Nomura Trust Bank, said the central banks' action may be aimed at cooling asset bubbles seen emerging in commodities and global stocks encouraged by easy monetary policy around the world.
The strength of the dollar's broad rebound may also depend on how much stock markets fall today, he said.
The market was further jolted on Friday by comments from Fed Board Governor Kevin Warsh that the U.S. central bank may have to raise interest rates from their currently ultra-low setting near zero percent before the need to take action is obvious, giving a boost to the greenback.
The euro fell 0.2 percent to $1.4638, away from its one-year peak of $1.4845 struck earlier this week on trading platform EBS.
Still, traders said Asian central banks had been buyers around $1.4620, putting a floor above Monday's lows around $1.4610.
Commodity prices likewise took a hit, dragging the Australian and New Zealand currencies lower.
Most Asian stock markets tracked Wall Street lower with Tokyo's Nikkei share average sliding 2.8 percent.
STERLING TUMBLES
Sterling was hammered after Bank of England chief Mervyn King said a weak currency was helping the domestic economy, which was taken as a green light for speculators to sell it.
The pound extended its slide on Friday when a break of major support at $1.6000 saw it collapse as far as $1.5917 before steadying around $1.5942, down 0.7 percent on the day.
The UK currency also sank against the euro, which rose more than 0.6 percent on the day to 91.93 pence, its highest since early April.
The dollar, on the other hand, fell 0.6 percent against the yen to 90.69 yen as the Japanese currency rose broadly, helped partly by its sharp gains versus the pound.
Against the yen, the euro shed 0.7 percent to 132.85 yen. Analysts said investors cut long euro positions versus the yen, which tended to rise when the market was confident about global growth prospects. (Additional reporting by Wayne Cole in SYDNEY; Editing by Chris Gallagher)