FOREX-Dollar's gains trimmed after U.S. private-sector jobs data

* Dollar benefiting from rise in U.S. yields this week

* ECB rate decision on Thursday overhangs market

* Slowdown in euro zone inflation seals case for ECB action

(Adds latest prices, ADP data details; changes dateline; previous LONDON) NEW YORK, June 4 (Reuters) - The U.S. dollar got a lift on Wednesday from rising Treasury rates and touched a monthly high against the yen before losing some steam on weaker-than-expected U.S. private-sector jobs numbers. The dollar last stood at 102.57 yen after trading as high as 102.79 yen, near a level last touched on May 5. The U.S. dollar index, composed of six major currency pairs, was last up 0.09 percent at 80.625 after peaking at 80.677. The dollar's early gains against the euro and other currencies were trimmed by the ADP National Employment Report, according to currency strategist Martin Schwerdtfeger at TD Securities in Toronto. Private employers added 179,000 jobs to their payrolls in May, ADP data showed. That compared with 215,000 jobs in April and was below economists' expectations for a gain of 210,000 jobs in May in the government's comprehensive employment report due on Friday. The ADP report does not have a good record predicting nonfarm payrolls, data that often shakes global currency markets, and it would have no lasting effect on trading, Schwerdtfeger said. "The market will be a little bit cautious to adopt any strong view," he said. Longer-dated U.S. Treasury yields have risen 20 basis points in the past week and the spread between two-year German and U.S. government bonds - the most directly responsive to interest rate moves - is within a whisker of its highest since mid-2007. The benchmark 10-year U.S. Treasury note was down 5/32, the yield at 2.6094 percent. Expectations the European Central Bank will take action on Thursday to support growth are hanging over the market, as such a move would put returns on euros in negative territory. That has caused the euro to bounce around in recent days, but the week's dominant trend is for a stronger dollar. Disappointment over the pace of U.S. economic growth in the first quarter meant the dollar defied views of banks and investment houses at the start of 2014 for a surge in its value. But expectations that the ECB will ease policy have reinforced the base case for a stronger U.S. currency, and that returns on U.S. government debt will rise while those in the euro area fall. The euro, which had been flirting with a $1.40 as recently as May 8, was off 0.08 percent against the dollar at $1.3615. Sterling was flat at $1.6750.

(Reporting by Michael Connor in New York; Editing by Dan Grebler)