* Brent slips to one-month low, WTI falls to two-week low
* API U.S. oil data shows draw of 1.1 mln barrels
* EIA raises U.S. crude output forecast for 2018
* Coming Up: U.S. EIA weekly inventory data Wednesday 1530 GMT (Updates with API figures, adds quote, updates bullets)
HOUSTON, Feb 6 (Reuters) - Oil fell for a third day on Tuesday as the U.S. dollar rose to its highest in more than a week in the wake of a sharp sell-off early this week on Wall Street and other stock markets.
The crude market remains in positive territory for the year however, even after Wall Street stocks on Monday posted their largest one-day fall since late 2011.
Brent crude futures for April delivery settled down 76 cents, or 1.12 percent at $66.86 a barrel, after touching a session low of $66.53, the weakest since Jan. 2.
U.S. West Texas Intermediate futures for March delivery dipped 76 cents, or 1.18 percent, to settle at $63.39 a barrel, the lowest since Jan. 22.
"Crude was acting like a puppet with the equity markets and dollar acting as the puppeteer," said Brian LaRose, senior technical analyst at ICAP.
U.S. crude futures were stronger in post-settlement trading after weekly inventory figures from industry group the American Petroleum Institute showed a 1.1 million barrel decrease in overall crude oil stocks for last week.
A preliminary poll by Reuters on Tuesday showed analysts expected weekly data to show U.S. crude inventories last week rose 3.2 million barrels.
"For oil, API's numbers are supportive. The market is going to try to determine if the crude draw offsets the distillate build heading into tomorrow's EIA report," said Phil Flynn, analyst at Price Futures Group.
Oil's inverse relationship to the dollar, whereby a stronger currency makes it more expensive for non-U.S. investors to buy dollar-denominated assets, has reasserted itself this week, with the greenback up more than 1 percent since Feb. 1.
The benchmark U.S. stock index, the S&P 500, has lost 6.2 percent since it hit a record high on Jan. 26. Oil has shed 5.2 percent.
U.S. stocks eventually rebounded in volatile afternoon trading on Tuesday. Major indexes rose more than 1 percent in a drastic swing after starting the session 2 percent lower from Monday. The difference between the high and low for the Dow on Tuesday was more than 1,100 points.
"With so much volatility in the equity markets people don't trust that rebound. Any time you get a 1,500-point move in one day that's going to spook markets," said Phillip Streible, senior market strategist at RJO Futures.
One factor that has lent support to oil prices is the structure of the forward curve. The prompt futures contract is trading well above those for delivery further in the future.
Oil prices have also been supported by a 1.8 million barrels per day (bpd) cut in supply by the Organization of the Petroleum Exporting Countries and Russia.
Still, rising U.S. supply has pressured oil. The U.S. Energy Information Administration said on Tuesday it expects domestic crude oil production in 2018 to rise by 1.26 million barrels per day (bpd) to an average of 10.59 million bpd. Last month, it forecast a 970,000 bpd year-over-year increase to 10.27 million bpd.
(Additional reporting by Amanda Cooper in London and Henning Gloystein in Singapore; Editing by David Gregorio)