* Euro inches up after euro zone inflation data
* Inflation rate not as bad as some had expected
* Soft EZ inflation supports expectations of ECB action (Updates after euro zone inflation data)
By Anirban Nag
LONDON, June 3 (Reuters) - The euro recovered from lows on Tuesday, after subdued euro zone inflation data kept alive the expectations of aggressive monetary stimulus from the European Central Bank, much of which is already priced in by investors.
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 was trading 0.1 percent higher at $1.3610, having fallen 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 ECB is widely expected to loosen policy when it meets 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.
Traders said for the euro to drop sharply, the dollar has to strengthen further. U.S. factory orders for April are due on Tuesday and a robust number may boost Treasury yields and help the dollar.
The dollar hovered near a four-month high against a basket of major currencies bolstered by recent upbeat U.S. data.
Trading was choppy in Asia, reflecting some confusion after the U.S. Institute for Supply Management corrected its manufacturing activity index for May to 55.4, from a below-consensus reading of 53.2. The ISM said it had to make the correction due to an error in applying the seasonal adjustments.
U.S. Treasury yields rose as a result, helping boost the dollar's allure. The dollar index stood at 80.593, within close reach of Monday's four-month high at 80.681.
"Following yesterday's U.S. data confusion, the dollar has maintained its recovery trend and we expect further broad-based gains today," Morgan Stanley said in a daily note.
"We maintain our long dollar strategies, with dollar/yen remaining the exception to the rule and where we have used the recent rebound to re-establish dollar short positions."
Against the yen, the U.S. currency was flat at 102.40 , having risen 0.6 percent on Monday in its biggest one-day rise in over two months.
The Australian dollar inched up after the Reserve Bank of Australia kept interest rates unchanged and refrained from trying to talk the currency down as some market watchers had speculated. It rose 0.3 percent to $0.9275. (Editing by Susan Fenton and Jane Merriman)