The Australian dollar rallied on Tuesday after an upbeat assessment of the global economy by the Reserve Bank of Australia spurred traders' appetite for high-yielding currencies, and the rising risk demand also helped boost the euro.

Higher risk appetite, combined with a lackluster U.S. service sector report, put the dollar under broad selling pressure amid fears of further slowdown in the U.S. economy.

The RBA held its key interest rate at 4.5 percent on Tuesday, saying policy was appropriate given caution in global markets even as it remained optimistic about the outlook for Asia and the domestic economy.

While the RBA had been widely expected to keep rates on hold, some investors had braced for a dovish statement after recent signs that the Chinese economy may be slowing.

Analysts said relief over the RBA position calmed investors and boosted global risk appetite, prompting an unwinding of extreme short positions in currencies such as the euro.

Risk appetite staged a strong turnaround, said Boris Schlossberg, a director for currency research at GFT Forex in New York. Although Australian monetary officials acknowledged the fact that global growth was slowing, they nevertheless remained positive regarding economic activity in Asia Pacific.

By late morning in New York, the Australian dollar had climbed more nearly 2 percent to $0.8543, pulling away from a session low of $0.8318.

The euro rose 0.8 percent to $1.2649, poking through option barriers at $1.26. The euro also briefly hit a two-week high against sterling, rising to as much as 83.14 pence.

In the United States, the dollar fell against the yen and the euro after the Institute for Supply Management said its measure of the U.S. non-manufacturing sector rose in June for a sixth straight month, but the rate of growth was at the lowest point since February.

The slowdown in the U.S. economy is real, the change in direction is serious, said Joseph Trevisani, chief market analyst at FX Solutions in Saddle River, New Jersey.

Statistics do not yet indicate a recession, but the mood is worrying. The dollar will continue to weaken, he said.

The dollar was last down 0.4 percent at 87.39 yen from 87.79 yen prior to the ISM release.

The euro also extended gains after the ISM report but currency analysts warned that investors should be cautious on the European currency.

Interbank borrowing rates in the euro zone remain elevated, said Brian Dolan at Forex.com.

SWISS FRANC RISES

The Swiss franc rose to as high as 1.0666 per dollar according to Reuters data, its strongest since mid-April, only to pull back to around 1.0580.

It was hit by data showing Swiss CPI rose 0.5 percent in June from a year ago, below the 1 percent rise analysts had forecast.  The franc was little changed at 1.3370 per euro, down from the day's high of 1.3282.

In June, the Swiss National Bank backed off a pledge to fight franc appreciation, saying deflation risks had faded.

Tuesday's improvement in risk appetite followed weeks in which it took a beating on growing worries about the health of the euro zone's banking system, a slowdown in China and the risk of a double-dip recession in the United States.

Clearly, people are feeling a little better about the world, but I am a pessimist, said Simon Derrick, head of currency research at Bank of New York Mellon. China could see a sharp slowdown toward the end of the year, which makes me think the bullish story is not as positive as it might look.

(Additional reporting by Nick Olivari and Wanfeng Zhou in New York and Naomi Tajitsu in London; Editing by Dan Grebler)