* Italy outperforms as Europe shares gain
* Wall Street set to rise after private sector jobs data
* Oil off 3-week lows before Trump decision on Paris accord
* Yuan hits 7-month high; China manufacturing contracts
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Nigel Stephenson
LONDON, June 1 (Reuters) - European stocks rose on Thursday with Italy setting the pace after a big upward revision in first-quarter economic growth, while the dollar rose after forecast-beating U.S. private sector jobs data.
Wall Street was expected to open higher, according to index futures , after the jobs numbers which are likely to feed into the Federal Reserve's interest rate decision later this month.
The pan-European STOXX 600 index edged up 0.3 percent, led higher by industrials and consumer staples companies. Bank shares lagged slightly after two major U.S. lenders, JPMorgan and Bank of America, warned on Wednesday that low market volatility would crimp trading revenue.
Italy's FTSE MIB index was the top gaining national market, up 0.6 percent and fractionally outperforming France's CAC 40.
Italy's national statistics bureau said strong domestic demand helped the economy grow 0.4 percent in the first quarter, twice as much as indicated by preliminary data issued last month.
The euro zone economy as a whole grew 0.5 percent in the period and, in a further sign of recovery, data on Thursday showed manufacturing grew in May at its fastest rate in six years.
Stronger euro zone data has helped push the euro higher against the dollar of late, contributing to the U.S. currency's worst fortnight since March 2016.
However, the greenback rose 0.4 percent on Thursday, hitting session highs after data showed the private sector added 253,000 jobs in May, above economists' forecasts. The ADP data comes a day before the more comprehensive non-farm payrolls report and a fortnight before the Fed is expected to raise interest rates.
Asian shares, as measured by MSCI's main index of Asia-Pacific shares, excluding Japan rose 0.1 percent, though gains were limited by data showing Chinese factory activity contracted in May for the first time in 11 months.
Chinese Shanghai Composite share index fell 0.5 percent after a private survey of the manufacturing sector. The findings contrasted with official data on Wednesday that suggested growth remained steady.
China's yuan, however, strengthened beyond 6.8 per dollar for the first time since Nov. 11 after the central bank pushed its reference rate, around which the spot rate can fluctuate, 0.8 percent higher in the second-largest single-day appreciation of the currency since it was de-pegged from the dollar in 2005.
Traders said major state-owned banks were selling dollars.
"The PBOC has let the yuan bulls loose in the China shop," said Stephen Innes, senior trader at OANDA in Australia, referring to the People's Bank of China.
Spot yuan last stood at 6.8066 per dollar, having strengthened as far as 6.7878 earlier. As recently as May 24, it traded at 6.8949 per dollar.
Britain's pound, on a rollercoaster ride this week as polls have sent conflicting signals about the outcome of next week's election, fell 0.2 percent to $1.2866 after another poll showed the Prime Minister Theresa May's Conservatives just 3 percentage points ahead of the Labour opposition.
There was little reaction to Britain's manufacturing PMI beating forecasts.
"This data point is clearly a positive for the UK economy however GBP traders are putting macro releases on the back burner at present, with the twists and turns in the race for upcoming election having a greater impact on the market of late," David Cheetham, markets analyst at broker XTB, said.
The euro was down 0.3 percent at $1.1209, having fallen as low as $1.1201 after the ADP data. The Japanese yen was down 0.5 percent to 111.32 per dollar.
Oil prices initially rose, lifting off Wednesday's three-week lows, after data showing a big drop in U.S. crude stocks last week, but pared gains as some participants doubted output cuts by OPEC would be enough to rebalance an oversupplied market.
Brent crude, the international benchmark for the oil market, was down 13 cents at $50.63 a barrel at 1243 GMT.
President Donald Trump is expected to announce later on Thursday whether he will withdraw the United States from the Paris accord on measures to fight climate change.
Phillip Futures' investment analyst Jonathan Chanes said a U.S. withdrawal would signal Trump's intention to further roll back emission regulations.
"That would favour the use and demand of fossil fuels," Chanes said.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Additional reporting by Nichola Saminather in SINGAPORE, Aaron Sheldrick in TOKYO, Ritvik Carvalho and Christopher Johnson in London; Editing by Tom Heneghan)