* European stocks down, euro gains respite after inflation data
* Data seen cementing case for ECB to ease policy
* Asian shares rise as U.S., China activity picks up
* Wall Street seen opening lower (Updates with fresh quotes, prices)
By Nigel Stephenson
LONDON, June 3 European shares dipped on Tuesday and the euro edged higher against the dollar after a fall in euro zone inflation cemented the case for the European Central Bank to ease monetary policy later this week.
The pan-European FTSE Eurofirst 300 equity index was down 0.5 percent at 1130 GMT, extending losses after data that showed annual consumer price inflation unexpectedly slowed to 0.5 percent in May.
Traders said expectations the ECB, which targets inflation of close to 2 percent, would cut interest rates on Thursday were already largely priced in and that only a weaker inflation number would have triggered a big market move.
The euro gained some respite on relief that price growth had not slowed even further, while German government bond futures fell.
"The inflation reading could have been much worse, but it nonetheless underpins the necessity for the ECB to act on Thursday," said Jeremy Stretch, head of currency strategy at CIBC World Markets.
Wall Street also looked set to open lower. S&P 500 index futures were down 0.2 percent
Expectations of lower euro zone rates, and recent upbeat U.S. economic data, have combined to push the euro to its weakest against the dollar since mid-February.
However, the single currency was up 0.1 percent at $1.3610, having fallen as low as $1.3587 immediately after the data, but still not far from a low of $1.3586 hit last week.
"A (ECB) refinance rate cut by 15 basis points and a negative deposit rate cut by 10 basis points is baked in. The risk is of a more aggressive cut in the deposit rate which has the potential to take the euro down below the $1.3585 level that has proved sticky in the past few sessions," Stretch said.
The dollar index, which measures the greenback against a basket of currencies, edged down but was close to Monday's four-month high.
The dollar stood at 102.40 yen, having earlier hit 102.49, its strongest in more than a month.
German 10-year government bond yields, which hit 12-month lows last week, rose 5 basis points to 1.36 percent. Bund futures declined. Some traders said the weak inflation data was already priced into the market and prompted investors to book profits after a recent rally.
"It's clearly a call for the ECB to take action but a lot of it is priced in already and there's a reluctance to take aggressive positions before the meeting. It (the ECB) will need to exceed expectations to drive yields lower" said Jan von Gerich, chief fixed income analyst at Nordea.
U.S. 10-year Treasury yields rose on Monday to 2.54 percent after the Institute of Supply Management showed U.S. manufacturing activity accelerated in May. The ISM data helped push U.S. stocks higher, with the Dow Jones average and S&P 500 index closing at record highs.
The U.S. numbers and Chinese data showing factory and service-sector performance had their best showings in months in May helped push Asian shares higher on Tuesday.
Japan's Nikkei hit a two-month high, further boosted by talk of public pension funds increasing their assets allocated to domestic shares. MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.4 percent, nearing a one-year high hit last week.
Emerging markets stayed broadly rangebound. Emerging dollar bond spreads versus Treasuries stood at 288 basis points , their tightest in 15 months. Emerging stocks rose 0.4 percent, just off recent 6-1/2 month highs
Gold snapped a five-day losing streak as shares fell, edging up 0.1 percent to $1.245.50 an ounce, but was still near a four-month low.
Brent crude slipped towards $108 a barrel, reflecting weak European demand, although the Chinese data kept a floor under prices. (Additiional reporting by Jamie McGeever, Sujata Rao and Sudip Kar-Gupta in London, Hideyuki Sano in Tokyo; Editing by Robin Pomeroy)