* Euro hits three-week high of $1.3294, Aussie recovers lost ground * Moves seen in thin trade, dollar should remain firm on U.S. outlook * Euro zone, China slowdown concerns hamper risk sentiment By Neal Armstrong LONDON, March 23 (Reuters) - The euro and the Australian dollar bounced back against the U.S. dollar on Friday as concerns over a slowdown in China and the euro zone eased slightly, but dealers said the greenback would be supported by the improving outlook in the United States. Worries about faltering global growth in the euro zone and China, which had hit stocks and riskier currencies a day earlier, eased off slightly tempering demand for safer bets such as the dollar and the yen. The dollar slipped to a three-week low versus the euro and the Swiss franc, also plumbing a two-week trough against a basket of currencies but traders said the sell-off was in thin liquidity and expected the greenback to hold firm. "We've definitely seeing a rotation of growth expectations with the U.S. outlook marginally better and China's outlook marginally downgraded. This should be positive for the dollar," said Geoff Kendrick, currency strategist at Nomura. "But it's been thin this week and the market still seems to be undecided which may explain the volatile moves. I think we need to see U.S. 10-year yields break above 2.4 percent for further dollar gains." U.S. 10-year notes yielded around 2.26 percent on Friday after stalling shy of 2.40 percent on Tuesday. Signs of improvement in U.S. economic conditions have boosted yields and the dollar in recent weeks. The dollar-index was down around 0.4 percent for the day after slipping to 79.214. It hit a two-month high of 80.738 earlier this month. The euro climbed from Thursday's low of $1.3133, rising to a three-week high of $1.3293 before dipping back to $1.3253, up 0.4 percent for the day. Many market players remain short of euros on worries over an economic slowdown and high levels of sovereign debt in many euro zone countries, notably Spain, but for now the common currency was gaining respite. "A week short on data and events is likely to end as it began - with illiquid trade and the resulting intraday jumps in EUR-USD. As a result any jerks up or down might easily knock market participants out of their positions in the range between 1.3000 and 1.3335," said Commerzbank in a note. YEN SLIPS The euro rose 0.6 percent to 109.55 yen, in the middle of the week's 108.49/111.57 range. Yen weakness was reinforced on selling by Japan importers, whose purchases of fossil fuels have surged as most nuclear reactors in the country were taken offline after the Fukushima disaster last year. The yen is likely to benefit from repatriation flows ahead of the Japanese fiscal year-end on March 31, but any gains could prove fleeting given how determined the Bank of Japan is to keep monetary policy ultra-loose. "While we could see some short-term bounce going into the fiscal year-end, the broad trend for the yen is lower," said Simon Derrick, head of currency research, at Bank of New York Mellon. "Given how successful the Bank of Japan has been in pushing the yen lower, they will look to pump additional funds and that will keep the yen weaker." The greenback has gained 7.5 percent against the yen since the start of this year, while the euro has jumped more than 10 percent, with gains picking after the Bank of Japan surprisingly eased policy by announcing more quantitative easing in February. The Australian dollar recouped some of this week's heavy losses against the yen to trade up around 0.1 percent on the day at 86.00 yen, but investors are likely to be cautious about perceived riskier currencies amid growing signs of a global slowdown. The Aussie moved further away from a two-month low of $1.0336 hit on Thursday to trade as high as $1.0450. Traders said stop-loss buy orders had been triggered at $1.0420/30, while Asian sovereign supply was noted around the highs as it later eased back below $1.0400.

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