* ISM data overshadows euro zone worries, lifts oil
* POLL-U.S. crude stocks down, product stocks up last week
* Coming up: API U.S. inventory data, 4:30 p.m. EDT Tuesday
NEW YORK, June 5 (Reuters) - U.S. crude oil futures rose for a second straight day on Tuesday as the vital U.S. service sector grew faster than expected in May, the ISM industry report showed - a small, bright lining that followed a spate of gloomy economic reports.
Gains were limited, however, as euro zone debt worries deepened after Spain said credit markets were cutting off the country. That pulled the euro lower against the dollar, deterring investors from making more bullish bets on oil futures.
Ahead of weekly inventory reports, U.S. crude stockpiles were forecast 500,000 barrels lower last week, a Reuters poll of analysts showed. If confirmed, the drawdown will snap 10 weeks of continuous increase.
Distillate stocks were expected to show a 300,000 barrel increase while gasoline stocks were seen likely up 700,000 barrels. Refinery utilization was predicted to have risen 0.6 percentage point.
The industry group American Petroleum Institute will release its inventory report at 4:30 p.m. EDT (2030 GMT). That will be followed by data from the U.S. Energy Information Administration, at 10:30 a.m. EDT, on Wednesday.
* On the New York Mercantile Exchange, crude for July delivery settled at $84.29 a barrel, rising 31 cents, or 0.37 percent, after trading between $83.31 and $84.92.
* In London, ICE July Brent crude oil futures finished 1 cent lower at $98.84 a barrel, trading between $97.68 and $99.63.
* U.S. crude's discount against Brent crude narrowed to $14.55, from $14.87 on Monday. CL-LCO1=R
* NYMEX July heating oil settled at $2.6336 a gallon, edging up 0.67 cent. It rebounded modestly after closing on Monday at $2.6269, the lowest close for front-month heating oil since Jan. 25, 2011.
* NYMEX July RBOB gasoline gained 1.40 cents to close at $2.6847. It ended down at $2.6707 on Monday, the lowest settlement for front-month gasoline since Dec. 28, 2011.
* The Institute for Supply Management said its services index for the U.S. economy edged up to 53.7 from 53.5 in April, a touch above economists' forecasts. A reading above 50 indicates expansion in the sector.
* U.S. retail gasoline demand fell 2 percent in the week to June 1, compared to the year-ago level as a dismal economic outlook weighed on fuel consumption, data from MasterCard's SpendingPulse report showed. Demand was 3.7 percent lower from the previous week, the report also showed.
* Purchasing managers' indexes showed that all of the euro zone's major economies were now in various states of decline, with the region's private economy shrinking in May at the fastest pace in nearly three years.
* Canadian oil output is poised to surge ahead far faster than expected only a year ago, the industry's main lobby group said, raising its forecast for 2020 production by half a million barrels a day. [ID: nL1E8H56WL]
* Oil prices will weaken in the second half of this year as demand reacts to a slowing global economy, while international political tensions ease, Royal Dutch Shell CEO Peter Voser said in Kuala Lumpur. <ID:nL3E8H51PU>
* Wall Street rebounded as data showing a slight growth in the U.S. service sector offset worries about the euro zone's fiscal crisis.
* The euro fell as Spain's treasury minister said high borrowing costs were closing the country off to credit markets and investors received scant comfort from an emergency conference call of Group of Seven finance chiefs.
* New York copper prices fell for a fifth straight day after a series of declining business surveys across Europe underscored a bleaker outlook for the global economy and industrial metal demand.
* Gold prices edged lower in light volume as the market paused from last week's rally.
UPCOMING EVENTS, DATA
* American Petroleum Institute's weekly U.S. petroleum inventory data, 4:30 p.m. EDT (2030 GMT), Tuesday.
* U.S. Energy Information Administration's U.S. petroleum supply data, 10:30 a.m. EDT (1430 GMT), Wednesday.
SETTLE NET PCT LOW HIGH CURRENT DAY AGO
CHNG CHNG VOL VOL CLc1 84.29 0.31 0.4% 83.31 84.92 229,965 309,777 CLc2 84.57 0.30 0.4% 83.61 85.20 46,448 64,637 LCOc1 98.84 -0.01 0.0% 97.68 99.63 141,152 174,173 RBc1 2.6847 0.0140 0.5% 2.6441 2.6911 38,102 61,931 RBc2 2.6141 0.0093 0.4% 2.5830 2.6221 32,981 25,622 HOc1 2.6336 0.0067 0.3% 2.6056 2.6443 35,603 59,042 HOc2 2.6404 0.0048 0.2% 2.6144 2.6516 17,044 18,253
TOTAL MARKET VOLUME OPEN INTEREST
CURRENT Jun 04 30D AVG Jun 04 NET CHNG CRUDE 448,439 580,789 535,372 1,446,448 -2,125 RBOB 105,960 121,446 151,954 288,232 6,074 HO 96,944 113,571 134,324 317,438 -902 (Reporting by Gene Ramos and Robert Gibbons; Editing by Marguerita Choy)