* Dollar steady after 2009 low vs euro, currency basket
* Global stock gains show improved risk appetite
* Data from U.S., China and Europe bolster optimism
* Policy meetings of RBA, ECB, BoE eyed
By Aiko Hayashi
TOKYO, June 2 (Reuters) - The dollar steadied on Tuesday a day after hitting its lowest this year against the euro and a basket of currencies as reassuring economic data and a rally on Wall Street reduced the safe-haven allure of the greenback.
The U.S. manufacturing sector improved in May to post its highest reading since September and construction spending in April notched its biggest increase in eight months, bolstering the view that the global economy is on the mend..
Generally upbeat manufacturing reports from the euro zone, Britain and China added to that optimism and fuelled a sell-off in the dollar on Monday.
Commodity-related currencies such as the Australian and Canadian dollars, considered to be higher risk, retreated from eight-month highs against the greenback set on Monday but still hovered near them as oil prices also jumped.
Traders said the market was likely to be range-bound, however, ahead of central bank meetings in Australia and Europe.
The Reserve Bank of Australia (RBA) holds a policy meeting on Tuesday and is expected to refrain from cutting interest rates for a second straight month from the record low of 3 percent.
The RBA will announce its decision at 0430 GMT along with a statement.
"Trade will likely be slow, at least until the end of the central bank meeting in Australia," said Minoru Shioiri, a senior manager of FX trading at Mitsubishi UFJ Securities.
The European Central Bank and the Bank of England hold policy-setting meetings on Thursday. Both are expected to hold short-term borrowing costs steady, and the ECB may provide more details on its plan to purchase assets to stimulate the economy.
"Profit-taking may also emerge in currencies that had gained quite a bit so far, such as the euro, if the central bank meeting in Europe mentions a rate cut or some unorthodox measures," Shioiri said.
DOLLAR UNDER PRESSURE?
The dollar index was steady at 79.154 after hitting its lowest since mid-December at 78.586 the previous day.
The euro was little changed from late U.S. trade at $1.4161, having rallied to $1.4246 on trading platform EBS on Monday, its strongest since late December.
Financial markets took in stride General Motors Corp's bankruptcy filing on Monday, the third-largest in U.S. history and the largest ever in the U.S. manufacturing sector.
"Still, as a general trend, players will likely opt for selling the dollar going forward," said Daisuke Uno, chief strategist at Sumitomo Mitsui Banking Corp.
"A string of factors that would prompt dollar selling still exists, including the U.S. credit problems and the restructuring of GM among others."
Higher risk currencies dipped from multi-month highs against the dollar as traders said their recent gains had been rapid and temporary profit-taking may be in store.
The Australian dollar fell 0.2 percent to $0.8086, retreating from an eight-month high of $0.8154. The New Zealand dollar eased to $0.6466.
Sterling was little moved at $1.6430, off a seven-month high it hit on Monday at $1.6497.
The dollar also fell 0.2 percent to trade at 96.40 yen, after rising as high as 96.81 yen the previous day. (Editing by Michael Watson)