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* Euro inches up after euro zone inflation data
* Inflation rate not as low as some had expected
* Soft EZ inflation supports expectations of ECB action
* U.S. Factory orders up for third straight month, gain 0.7 pct in April (Updates with U.S. factory order data, changes byline, dateline, previous LONDON)
By Daniel Bases
NEW YORK, June 3 (Reuters) - The euro held gains against the U.S. dollar on Tuesday, recovering ground as subdued euro zone inflation data kept market expectations for European Central Bank stimulus measures intact ahead of Thursday's meeting.
Stronger-than-expected U.S. factory orders in April, a third straight month of gains, meanwhile supported the view the U.S. economy continued to rebuild and recover.
"The U.S. data certainly supports the idea that the U.S. economy is going to have a nice bounce-back in the second quarter, but truthfully it is Europe that is the driving force this week," said Andrew Dilz, currency trader at Tempus Inc., a Washington, D.C.-based corporate foreign exchange trading house.
The euro rose 0.25 percent at $1.3628 while holding a at 139.67 yen, a gain of 0.35 percent.
"We, like most everyone else, expect (ECB President Mario) Draghi to announce some easing. That should push us below $1.36 which is something we've been testing. We're looking at $1.35/25, assuming he announces some kind of (quantitative easing) or rate cut," said Dilz.
The ECB is widely expected to loosen policy on Thursday. Measures are expected to include negative deposit rates, the rates at which banks park excess cash with the ECB, and that could see the euro come under more pressure, analysts said.
Earlier, annual consumer inflation in the 18 countries sharing the euro fell to 0.5 percent in May from 0.7 percent in April, data showed on Tuesday. Economists surveyed by Reuters expected inflation to remain at April's level.
But a number of big banks had already slashed their forecasts to 0.5 percent after soft German numbers on Monday.
With most speculators already running big bets against the euro, traders said, only a weaker-than-expected inflation reading of 0.4 percent or lower would have taken the euro towards $1.3580 - levels last seen in mid-February.
The euro fell to $1.3587 immediately after the inflation data was released, taking it close to a 3-1/2 month trough of $1.3586 plumbed late last month.
"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 Market.
"A 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."
The dollar eased back from Monday's four-month high against a basket of currencies made up of its major trading partners, but remain within striking distance of that level.
The dollar was up just 0.10 percent at 102.46 yen. (Editing by Susan Fenton, Jane Merriman and Meredith Mazzilli)