* API to report storage estimates on Tuesday, EIA on Wednesday
* 2018 oil demand to rise by 1.59 mln bpd to 98.6 mln bpd - OPEC
* IEA raises demand growth forecast to 1.4 mln bpd in 2018 (Updates prices, adds comment)
LONDON, Feb 13 (Reuters) - Oil fell on Tuesday, losing gains made earlier in line with a recovery on global stock markets, after a forecasting agency estimated world crude supply could overtake demand this year, potentially undermining producer efforts to curb supply.
The Paris-based International Energy Agency raised its forecast for oil demand growth in 2018 to 1.4 million barrels per day, from a previous projection of 1.3 million bpd.
However, rapidly rising output, particularly in the United States, could well outweigh any pick-up in demand and begin to push up global oil inventories, which are now within sight of their five-year average.
"Today, having cut costs dramatically, U.S. producers are enjoying a second wave of growth so extraordinary that in 2018 their increase in liquids production could equal global demand growth," the IEA said.
Brent crude futures were down 23 cents at $62.36 a barrel by 1318 GMT, while U.S. West Texas Intermediate crude futures were down 40 cents at $58.89.
"Overall, the IEA confirms its bearish view on global supply and demand, expecting no significant global stock draws in 2018," Petromatrix strategist Olivier Jakob said.
"OPEC has a more bullish view but has been forced to reduce its call-on-OPEC estimate over the last few months and it has the risk of showing further reductions since its forward outlook for U.S. crude seems to be unrealistically low."
The Organization of the Petroleum Exporting Countries said on Monday it expected world oil demand to climb by 1.59 million bpd this year, an increase of 60,000 bpd from the previous forecast, reaching 98.6 million bpd.
European equity markets were broadly steady, as gains in travel and leisure stocks offset losses in telecoms. Last week's volatile trading had seen major indexes record some of their biggest one-day falls.
The private American Petroleum Institute is due to publish crude inventory estimates on Tuesday, while the U.S. government's Energy Information Administration releases fuel storage and crude production data on Wednesday.
"The much-watched U.S. inventory levels are set to increase seasonally over the coming weeks as refineries go into maintenance," Julius Baer's head of macro and commodity research, Norbert Ruecker, said.
"This should challenge the still-prevalent market tightening narrative at least temporarily. We see more downside for oil prices and stick to our short position."
In an effort to tighten markets and prop up prices, OPEC and other producers including Russia have been withholding supplies since 2017. The cuts are scheduled to last through 2018.
(Additional reporting by Henning Gloystein in Singapore; Editing by Dale Hudson)