TOKYO, June 22 (Reuters) - The euro slipped on Tuesday, giving back gains made after China set the yuan's mid-point at its highest since the yuan's revaluation in 2005, as players wondered how fast the Chinese authorities would let their currency rise.

The euro and the Australian dollar hit their highs for the day after China's central bank set the yuan's daily mid-point at 6.7980 against the dollar, stronger than Monday's 6.8275 per dollar. Traders took it as a sign it could allow the yuan to rise further.

The rise in the euro and the Australian dollar was short-lived, however, as spot yuan CNY=CFXS eased against the dollar after soaring to its highest level since its July 2005 revaluation.

The euro and the Aussie slipped simply because the yuan eased, with some players suspecting Chinese authorities might be intervening to rein in the yuan's rise, said a senior FX trader at a big Japanese brokerage.

The market took the yuan 0.42 percent higher on Monday, its biggest one-day rise since the 2005 revaluation. But dealers fear the central bank will not let the market keep boosting the yuan at the pace seen the previous day.

The euro EUR= dipped 0.1 percent to $1.2298, off the day's peak of $1.2355. It hit a one-month high of $1.2490 on trading platform EBS on Monday after China pledged to allow the yuan to rise, boosting confidence in the global economy.

Near-term support was seen at $1.2253, a 38.2 percent Fibonacci retracement of the rise from a four-year low of $1.1875 on June 7 to Monday's high of $1.2490.

On the other hand, the dollar index .DXY was up 0.1 percent at 86.01, holding well above support at 85.13. The index posted a bullish reversal on Monday, suggesting more gains for the greenback in the near term.

Beijing's vow of flexibility for the yuan, which should boost purchasing power and demand in the the world's third-largest economy, had initially fuelled a rally in risky assets on Monday.

But the rally ebbed with not much follow-through buying, with China's move undertaken primarily for political purposes, analysts said. Leaders of the Group of 20 leading industrialised and developing economies are to meet next week in Toronto, where global trade imbalances are expected to be a key issue.

China on Monday ruled out a one-off revaluation and said it will reform its exchange rate regime in a gradual manner.

The Chinese decision provided a welcoming short-term distraction in a market gripped by fear and anxiety, but the underlying European fiscal headaches and global growth uncertainties remain unaltered, wrote Matthew Strauss, currency strategist at RBC Capital.

Some traders said they expect the yuan to be a short-term trading factor until a bigger trend comes to the market.

RBC's Strauss said the euro's failure to break past resistance near $1.25 was likely to result in a period for weakness for the single currency. Against the yen, the euro was down 0.3 percent at 111.94 EURJPY=R, having shed about 0.2 percent on Monday.

The euro in recent months has moved with swings in risk appetite. On Monday, the 25-day rolling correlation between the euro and the S&P 500 .SPX was at a robust 54 percent.

The fading risk rally was also evident in stock markets.

The Australian dollar AUD=D4, which had gained 1.4 percent in the previous session, was at $0.8785, with support at $0.8750 -- Monday's low -- and strong resistance at Monday's $0.8860 high.

The Aussie jumped to hit the day's peak at $0.8834 after the yuan mid-point fixing. (Additional reporting by Anirban Nag in Sydney and Satomi Noguchi in Tokyo; Editing by Chris Gallagher)