* EIA cuts U.S. oil production forecast for 2018
* European refineries boost crude intake in June
* European stocks of diesel and other oil products slid
* Goldman Sachs warns of oil below $40 per barrel
* Saudi Arabia produces a little more oil in June than OPEC target
* Coming up: API U.S. inventory data, 4:30 p.m. EDT/2030 GMT (Adds latest prices, U.S. EIA STEO production forecast)
NEW YORK, July 11 (Reuters) - Oil prices climbed more than 1 percent on Tuesday along with rising heating oil futures on reports showing forecast cuts in U.S. oil production and a decline in European product stockpiles.
Those price increases came ahead of weekly data expected to show U.S. crude stocks fell 2.9 million barrels while gasoline and distillate stocks each rose by 1.1 million barrels, according to a Reuters poll.
The American Petroleum Institute (API) will issue its petroleum storage report at 4:30 p.m. EDT (2030 GMT) on Tuesday. That will be followed by the U.S. Energy Information Administration's (EIA) report at 10:30 a.m. EDT on Wednesday.
Benchmark Brent futures rose 64 cents, or 1.4 percent, to settle at $47.52 a barrel. U.S. West Texas Intermediate crude also rose 64 cents, or 1.4 percent, to settle at $45.04 per barrel.
U.S. heating oil futures, meanwhile, gained 1.6 percent on Tuesday, boosting the products crack spread <CL321-1=R>, a measure of refinery margins, to the highest since late May.
European refineries increased crude oil intake in June, but stocks of oil products, particularly diesel, slid, Euroilstock data showed on Tuesday.
"That tells you demand globally is a lot stronger than people thought it was going to be and that is having a net positive effect on heating prices," said Scott Shelton, energy specialist at energy brokerage ICAP in Durham, North Carolina.
In a separate report on Tuesday, EIA projected U.S. crude oil production in 2018 will rise by less than previously expected.
Traders noted Tuesday's crude price declines were mitigated by reports Saudi Arabia exceeded its OPEC production target and notes from banks lowering oil price forecasts for this year and 2018.
BNP Paribas slashed its forecasts for Brent by $9 to $51 a barrel for 2017 and by $15 to $48 for 2018. Barclays cut its 2017 and 2018 Brent forecasts to $52 a barrel for both years from $55 for 2017 and $57 for 2018.
Crude prices remain about 16 percent below 2017 opening levels despite a deal led by the Organization of the Petroleum Exporting Countries to cut production from January.
OPEC agreed with Russia and some other major exporters to cut output about 1.8 million barrels per day until March 2018. But production elsewhere has risen as OPEC has held back.
U.S. oil production <C-OUT-T-EIA> has jumped more than 10 percent over the last year to 9.34 million bpd. Nigeria and Libya, OPEC members exempt from production limits, have also increased output.
Saudi Arabia's oil production in June rose to 10.07 million bpd, putting it about 12,000 bpd over its OPEC output target.
Without a significant fall in oil inventories or a decline in U.S. drilling and production, Goldman Sachs said U.S. crude could drop below $40 per barrel.
(Additional reporting by Christopher Johnson in London and Henning Gloystein in Singapore; Editing by David Gregorio and Diane Craft)