* Recovery in equities markets supportive to crude prices
* Russia looking at joint organization for cooperation with OPEC
* Market awaits U.S. production data for fresher cue
* Coming up: API inventory data (Recasts lead, refreshes prices, adds comments; changes byline, dateline, previous LONDON)
NEW YORK, April 3 (Reuters) - Oil edged up on Tuesday, supported by a recovery in the equities market but still struggled to shake off the biggest one-day percentage drop in almost a year on Monday.
Wall Street's main indexes were higher on Tuesday as technology and consumer discretionary stocks recovered. The Dow and the S&P opened above their 200-day moving averages after the S&P 500 on Monday broke below that important level for the first time since Britain's vote to leave the European Union in June 2016.
"The oil complex is reviving a close correlation with equity swings now that shifts in the stock market have proven too large to ignore," Jim Ritterbusch of Ritterbusch and Associates said in a note.
Brent crude futures were up 44 cents at $68.08 a barrel by 11:43 a.m. EDT (1643 GMT) on Tuesday. This followed a nearly 4 percent drop in Brent prices on Monday, the largest since June.
Brent rose to $71 a barrel last week, close to its highest this year, but failed to hold on to that level.
West Texas Intermediate futures also rose 44 cents to $63.45 a barrel.
Also lending support was Russian Energy Minister Alexander Novak's comments on Tuesday that a joint organization for cooperation between OPEC and non-OPEC countries may be set up once the current deal on oil output curbs expires at the end of this year.
Limiting price gains, however, was an expected increase in U.S. crude inventories.
U.S. crude inventories, widely viewed as a litmus test of the broader trend in global inventories, are expected to have risen by 1.7 million barrels in the week to March 30, according to a Reuters poll..
The American Petroleum Institute releases its weekly inventory data later on Tuesday and the U.S. government releases its figures on Wednesday.
There is also an element of seasonality at play, said Walter Zimmerman, chief technical analyst at United-ICAP. "Yesterday was a little more dramatic than might typically be the case, but it's entirely in keeping with seasonal peaking risk that the month of April brings to crude oil," he said.
Also weighing on the market is speculative length, after money managers last week raised their bullish bets on crude.
"With excessive hedge fund positions still looming over the market, profit-taking should weigh on oil prices over the coming weeks," Julius Baer head of commodities and macro research Norbert Ruecker said.
Prices for physical barrels of oil in the North Sea are around their lowest since last June, as extensive refinery maintenance across the region eats into demand.
(Additional reporting by Amanda Cooper in London, Meng Meng in Beijing and Henning Gloystein in Singapore; Editing by David Evans and Tom Brown)