* U.S. dollar index rebounds from 2009 low, yen rises
* Euro falls from 7-1/2-week high versus dollar
* U.S. consumer confidence declines by more than expected
* Details of the two-year auction dollar-negative (Adds comments, updates prices)
By Gertrude Chavez-Dreyfuss
NEW YORK, July 28 (Reuters) - The dollar recovered from its lowest level of the year against a currency basket on Tuesday as weak consumer confidence rekindled worries about the stability of the U.S. economy's recovery, increasing safe-haven demand for the greenback.
The yen also rallied across the board as investors dumped riskier assets. The lower-than-expected U.S. consumer sentiment index added to pessimism that was already evident in financial markets amid disappointing quarterly results from a handful of major companies such as Office Depot Inc.
That weighed heavily on stocks and oil and dragged down the Australian dollar from its highest level against the U.S. currency since September.
"There's a pullback in risk appetite with the U.S. consumer confidence data and that's why we're seeing the yen and dollar gaining," said Vassili Serebriakov, senior currency strategist at Wells Fargo in New York.
"The data suggests recovery signs in the U.S. are mixed and today's second straight decline in consumer confidence shows the consumer is still fragile and vulnerable."
In late afternoon trading, the ICE Futures' U.S. dollar index, which measures the performance of the greenback against a basket of currencies, rose 0.3 percent to 78.897. It had fallen to 78.315, its lowest since December.
The euro fell 0.5 percent to $1.4168, having climbed as high as $1.4303, its highest since early June, according to Reuters data.
Analysts said the euro zone single currency's losses also reflected unwinding of huge euro long positions by speculative traders. Data from the Commodity Futures Trading Commission last Friday showed speculators more than doubled their euro bets in the week ended July 21, to 34,772 contracts. That was the largest euro long position since March 2008.
OVERBOUGHT MARKETS
"We've had a nearly two-week run-up in stocks and a flight into riskier currencies. Markets are kind of technically overbought in terms of risk and due for a bounce," said David Gilmore, a partner at Foreign Exchange Analytics in Essex, Connecticut.
Against the yen, the dollar fell 0.6 percent to 94.63 yen, while the euro dropped 1.1 percent to 134.07 yen.
Yen and dollar buying increased after U.S. consumer confidence fell more than expected in July, Conference Board data showed, in a second straight decline.
That nullified a Standard & Poor's/Case Shiller report showing U.S. single-family monthly home prices rose in May, the first increase in nearly three years.
Wells Fargo's Serebriakov said even though consumer confidence dropped, there are "encouraging signs that the housing market may be finding a bottom." On balance, he thinks the worst of the global financial crisis has passed.
A $42-billion two-year Treasury auction on Tuesday, meanwhile, had little impact on the currency market although details of the outcome were not encouraging for the dollar. Indirect bidders, a key gauge of foreign interest, accounted for just 32.6 percent versus a three-auction average of 51 percent.
In addition, the market tail on the auction printed 3.3 basis points, suggesting investors required a premium above the market rate. Analysts said this trend will likely continue in the months ahead as a swelling U.S. deficit prompts investors to demand a higher rate of return for Treasuries.
The Australian dollar rallied to a high of US$0.8338 after Australia's central bank governor fueled speculation interest rates may rise soon.
Reserve Bank of Australia Governor Glenn Stevens said risks to the economy were now more balanced and low rates could inflate a housing bubble. Analysts said Stevens gave the clearest signal yet the RBA was likely done with easing. (Additional reporting by Wanfeng Zhou; Editing by James Dalgleish)