The euro and Australian dollar rebounded from early losses against the dollar and yen on Tuesday after a statement by Australia's central bank helped dispel some gloom about the economic outlook and led to short-covering.

The Reserve Bank of Australia (RBA) left its cash rate steady at 4.5 percent as expected, saying the global economy had continued to expand, albeit unevenly, with growth in Asia very strong and signs of China moderating to a more sustainable rate.

The Aussie fell in thin trading ahead of the announcement as some had expected it to sound a more dovish note, and on the charts it formed a short-term double bottom at $0.8317 AUD=D4, a drop which helped set it up technically for a rebound.

There were concerns among dealers that the RBA would be very bearish about the economy before the rate announcement. But the central bank was not that dovish, prompting players to buy back the Australian dollar, as well as the euro, Daisuke Karakama, market economist at Mizuho Corporate Bank.

But there were no new factors out. The only thing we can say is that the euro and the Aussie are in a rebound phase.

The Aussie stood 0.4 percent up on the day at $0.8437 AUD=D4 after earlier dropping to test support at $0.8315, a low set last week.

Against the yen it climbed 0.6 percent on the day at 74.08 yen AUDJPY=R after sliding as far as 72.73 yen.

The RBA is refusing to panic, as many in the market seem to be, said Brian Redican, senior economist at Macquarie.

Some analysts said another rate hike in August could not be ruled out but a rate cut, as some had started to talk about, looked unlikely.

Yes, global uncertainties are to the downside, so that raises the bar for a hike. But the RBA is still sounding confident and there's very little chance of a cut, Redican said.

Global risk appetite has taken a beating in the past few weeks on growing worries about the health of the euro zone's banking system, a slowdown in China and risks of a double-dip recession in the United States.

The euro, which dipped to $1.2479 in early trade, pulled back up to $1.2557 EUR=, heading back towards last week's six-week high at $1.2613.

Against the yen it also turned positive at 110.28 yen EURJPY=R after dipping as far as 109.14 early on.

The early losses came after Harvard University economist Kenneth Rogoff, a former International Monetary Fund chief economist and an expert on banking crisis, told Bloomberg Television that China's property market is beginning a collapse that would hit banks.

The report fed into concerns about China's economy, while speculative trades exaggerated yen gains in subdued activity as the market awaited the return of U.S. players from a long weekend.

U.S. markets were closed for the Independence day holiday on Monday.

Data from Japan's finance ministry showed China expanded its buying of Japanese government bonds in the first four months this year, buying a net 541 billion yen of mostly short-term JGBs, double a record amount logged in 2005, amid the euro zone debt crisis.

JGB market players said the buying was probably more about parking funds short-term during the euro zone debt crisis than long-term interest.

The dollar index, a gauge of the greenback's performance against a basket of six major currencies, slid 0.2 percent to 84.427 .DXY. The index's near-term support is seen at 84.132, a seven-week low hit last week.

The dollar was steady at 87.75 JPY= with the market watching whether it could hold above 87.00 yen JPY= as options triggers are believed to be set below that level, traders said.

The greenback hit a seven-month trough of 86.96 yen last week on the back of growing worries about an economic slowdown in the United States. (Contribution by Reuters FX analyst Krishna Kumar; Editing by Joseph Radford)