* Aussie gains 1 pct vs dollar, yen after upbeat RBA outlook
* Higher shares show improving risk demand, boosting euro
* Dlr broadly lower, briefly hits 3-mth low vs Swiss franc (Adds comment, updates prices)
By Naomi Tajitsu and Lin Noueihed
LONDON, July 6 (Reuters) - The Australian dollar rallied on Tuesday after an upbeat assessment of the global economy by the Reserve Bank of Australia, while receding sovereign debt fears and rising risk demand helped boost the euro across the board.
This put the dollar under broad selling pressure, pushing it to a three-month trough versus the Swiss franc. The franc later fell after weak Swiss consumer price data tempered the view that deflation risks had faded.
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. [ID:nSGE66508X]
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 risk appetite, prompting an unwinding of extreme short positions in currencies such as the euro.
"The RBA statement showed no sign of the fears priced in by the market. It was a balanced statement," said Elsa Lignos, currency strategist at RBC. "It is now very unlikely that we will see more cuts this year and in fact there could be hikes."
By 1105 GMT, the Australian dollar AUD=D4 had climbed 0.96 percent to $0.8479, pulling away from a session low of $0.8317.
The euro EUR= rose 0.30 percent to $1.2576, poking through option barriers at $1.26. The euro also briefly hit a two-week high against sterling, rising 0.2 percent to 83.10 pence after failing to break above 83 pence for the past two sessions.
The euro has struggled to make major gains above $1.2600, however, with traders citing stop-loss orders above $1.2610. The formation of an Ichimoku "cloud" around $1.2576 has also constrained the single currency.
Ian Stannard, senior foreign exchange strategist at BNP Paribas, said there was potential for the euro to gain broadly and move towards a new target of 84 against sterling as he expected a European Central Bank statement on Thursday to comfort markets. He also said positive results from stress tests of euro zone banks due later this month would boost euro.
"I see euro/sterling performing particularly well," he said.
SWISSIE HIT BY DATA
The Swiss franc CHF= rose to 1.0563 per dollar in early European trade according to Reuters data, its strongest since mid-April, only to pull back to around 1.0625.
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.[ID:nZAT010924] The franc EURCHF= was flat against the euro at 1.3365 per euro, down from the day's high of 1.3282.
"This does put the CPI back on track towards deflation. The SNB must be wondering how to get out of this trap," Lignos said.
"I don't think they will be pushed to act on one data point but this CPI does suggest that, despite their recent comments, deflation is back on the table."
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 risks 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 towards the end of the year, which makes me think the bullish story is not as positive as it might look."
(Additional reporting by Tokyo Forex Team, editing by Nigel Stephenson)