* Dollar rises broadly vs major currencies at quarter-end

* DXY on track for biggest quarterly gain since 2008 (Updates prices, adds comments)

By Masayuki Kitano

SINGAPORE, March 31 (Reuters) – The dollar rose against a basket of currencies on Tuesday and was on track for its best quarter since 2008, bolstered by the diverging outlook for monetary policy in the United States compared to other major economies.

The greenback remains below peaks hit earlier in March, having given back some ground over the past couple of weeks after the U.S. Federal Reserve signalled a more cautious outlook for U.S. economic growth.

Still, the dollar has been supported by expectations that the Fed will start tightening monetary policy later this year. That poses a stark contrast to policies in the euro zone and Japan, where central banks are engaged in quantitative easing to support economic growth.

The dollar index, which measures the greenback’s value against a basket of major currencies, rose 0.2 percent to 98.214 and was up 8.8 percent for the quarter, putting it on track for its best quarterly performance since the third quarter of 2008.

The dollar gained broadly against major currencies on the last day of the January-March quarter.

The euro fell 0.4 percent on the day to $ 1.0791.

The euro has fallen about 10.8 percent this quarter, having been pressured by the launch of the European Central Bank’s quantitative easing programme.

Against the yen, the dollar edged up 0.1 percent to 120.17 yen, holding firm after having gained 0.8 percent on Monday for its biggest one-day rise in more than a month.

The bounce offered hope that its recent slide from a near eight-year peak of 122.04 to 118.33 might have run its course for now, although some analysts said its advance may be limited in the near term.

The dollar is likely to trade in a 118 yen to 122 yen range for a while, said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore.

“The (dollar’s) topside will probably be limited,” Okagawa said, adding that a recent drop in U.S. bond yields may help temper the greenback’s gains versus the yen for now.

The 10-year U.S. Treasury yield is now near 1.95 percent , down from a two-month high of 2.259 percent touched in early March.

The Australian dollar fell 0.3 percent to $ 0.7634, edging back in the direction of a near six-year low of $ 0.7561 set earlier in March.

Persistent weakness in commodity prices, worries about slower Chinese growth and expectations of interest rate cuts at home have conspired to knock the Aussie lower.

In contrast, U.S. data on Monday provided a more benign backdrop for the greenback. An industry report showed a pick up in home sales, while a measure of core inflation quickened to 1.4 percent, from 1.3 percent, in the 12 months through February.

“This should reassure the Fed that recent low headline inflation readings are the result of transitory energy price declines and that inflation is likely to rise toward the Fed’s target over time,” said John Ryding, chief economist at RDQ Economics in New York.

Disappointingly, U.S. consumer spending barely rose in February, the latest sign that a harsh winter had slowed the economy in the first quarter. Still, many investors are betting the economy would bounce back smartly.

(Additional reporting by Ian Chua in Sydney; Editing by Kim Coghill)