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UPDATE 6-Oil rises as global markets stabilize, dollar slips

* Firmer oil market comes after week of heavy losses

* U.S. crude holds near $60 per barrel as output soars (Updates throughout, changes dateline, previously LONDON)

NEW YORK, Feb 12 (Reuters) - Oil rose on Monday, as it began to recoup some of last week's steep losses as global equities steadied after their biggest one-week decline in two years.

Brent crude futures rose 67 cents, or 1.1 percent, to $63.46 a barrel by 10:55 a.m. EST 1/81555 GMT 3/8. U.S. West Texas Intermediate crude futures for March delivery rose 77 cents to $59.97 a barrel, a 1.3 percent gain. Earlier in the session, U.S. crude rallied to $60.83.

A weaker dollar helped to support oil by making dollar-priced crude cheaper for holders of other currencies.

The crude market was also supported after traders had unwound long positions last week, and looked to regain some long footing early this week, said John Macaluso, analyst at Tyche Capital Advisors.

Early in the week, the market is likely to be driven by technical factors before fundamental inventory data from the U.S. Energy Information Administration kicks in later in the week, he said.

"Were two days away from EIA numbers, where were probably going to see another build," he said.

Consumption remains robust, even though rising U.S. crude production has knocked oil off its 2018 highs above $70 and threatened the efforts of the Organization of the Petroleum Exporting Countries to prop up prices by reining in supply.

"Demand growth is very strong and, with (output) declines in places like Venezuela, is helping the situation. If demand stays strong, it still looks like OPEC will be in control in 2019," said SEB chief commodities strategist Bjarne Schieldrop.

"If global growth does slow down and oil demand starts to slow, then production growth in the U.S. becomes a problem, because OPEC's cake starts to shrink and that will be the line in the sand."

U.S. oil production <C-OUT-T-EIA> has risen above 10 million barrels per day (bpd), overtaking top exporter Saudi Arabia and coming within reach of top producer Russia.

OPEC and partners including Russia have agreed to cut their crude output by 1.8 million bpd for a second year, but U.S. production looks set to continue to grow.

U.S. energy companies added 26 oil rigs looking for new production last week, boosting the count to 791, the highest since April 2015, energy services company Baker Hughes said on Friday.

"We stick to our bearish view and see more downside for oil prices. The U.S. shale boom shows strong momentum and U.S. inventory levels are set to increase seasonally over the coming weeks as refineries go into maintenance, which should challenge the still-prevalent market tightening narrative at least temporarily," Julius Baer head of macro and commodity research Norbert Ruecker said in a note.

PVM Oil Associates strategist Stephen Brennock said these are tough times for oil bulls.

"Positives may appear in short supply but, along with OPEC-led production curbs, buyers can take solace from a healthy global oil demand backdrop. Much of this is owing to Chinas ravenous thirst for oil, which saw it surpass the U.S. to become the worlds largest crude importer in 2017," he said.

(Additional reporting by Henning Gloystein in SINGAPORE; Editing by Marguerita Choy and Susan Fenton)