* Euro weakens as ECB clings to tame inflation outlook
* Crude recovers as U.S. inventory draw overshadows no OPEC deal
* U.S., European stocks rebound with oil; Japanese shares drop
* Safe-haven bids stoke demand for U.S., German bonds (Update market action,)
By Richard Leong
NEW YORK, June 2 (Reuters) - The euro declined on Thursday on the European Central Bank's cautious economic outlook, while oil prices recovered on a drop in U.S. crude inventories, erasing losses on OPEC's failure to reach a deal to set an output ceiling.
The crude market rebound lifted Wall Street and European stocks out of the red, removing the earlier sting from a 2 percent slump in Japanese shares.
U.S. and German government bond prices firmed on safe-haven bids as a possible U.S. interest rate increase and the June 23 referendum whether Britain would leave the European Union, or "Brexit," posed near-term risks that could rattle investors.
"The bigger looming issue is the Brexit question. If it comes to pass, it would help calm markets," said Matt Kaufler, portfolio manager at Federated Investors in Rochester, New York.
The ECB nudged up its inflation forecast for 2016 but predicted price growth would remain below target through 2018 as depressed energy costs have held down prices of other goods and services. group of the world's major oil exporters failed to come to an output policy, with Iran insisting on the right to ramp up production. by OPEC's inability to clinch a deal addressing the global supply glut and sluggish demand, traders initially sold oil futures. Buying later emerged in reaction to government data showing a drop in U.S. oil inventories. crude futures CLc1 settled up 16 cents or 0.33 percent at $49.17 a barrel, while Brent oil futures LCOc1 settled up 32 cents or 0.64 percent at $50.04.
The disinflationary effect of cheap oil on the euro zone, together with weak regional growth, will likely lead the ECB to stick to its negative interest rate policy for a protracted period. This ultra-loose policy stance would undercut the euro. euro was down 0.35 percent at $1.1147 EUR , fading from its highest against the greenback in over a week. It lost 1 percent at 121.31 yen after hitting its weakest against the yen since April 2013 EURJPY= .
The euro's decline offset dollar weakness against the yen and other major currencies. The dollar index .DXY was little changed at 95.378.
The rebound in oil prices boosted U.S. energy stocks, helping reverse initial losses of major market indexes.
The Dow Jones industrial average .DJI fell 33.42 points, or 0.19 percent, to 17,756.25, the S&P 500 .SPX slipped 5.3 points, or 0.25 percent, to 2,094.03 and the Nasdaq Composite .IXIC declined 7.77 points, or 0.16 percent, to 4,944.48.
Europe's broad FTSEurofirst 300 index .FTEU3 eked out a 0.05 percent gain at 1,350.99.
Earlier, Tokyo's Nikkei .N225 tumbled 2.3 percent.
The MSCI world equity index .MIWD00000PUS , which tracks shares in 45 nations, dipped 0.06 percent to 401.94.
In the bond market, the benchmark 10-year Treasury note US10YT=RR was up 11/32 in price to yield 1.808 percent, after touching its lowest level in two weeks. 10-year Bund yield DE10YT=RR fell nearly 2 basis points at 0.118 percent.
Spot gold prices XAU= fell $1.34 or 0.11 percent, to $1,211.06 an ounce.