* Prices jump on late surge after sharp volatility earlier
* Brent and U.S. crude still down on week
* OPEC keeps output unchanged in oversupplied market
* Relief rally after losses of past two days
* Dollar rise on jobs report initially hampered oil gain (Adds rig count data in final paragraph)
By Barani Krishnan
NEW YORK, June 5 (Reuters) - Oil staged its first rally in three days on Friday, gaining 2 percent, despite warnings of more oversupply as a result of OPEC’s decision to keep pumping crude without restraint.
A strong dollar, which often depresses commodity prices, failed to stem the late runup in Brent and U.S. crude futures, despite limiting their gains in choppy early trade.
“I guess some people wanted to take their oil shorts off before the weekend and put them on again next week,” said Tariq Zahir, an oil bear at Tyche Capital Advisors in Laurel Hollow, New York. “Otherwise how do you have a runup on a day like this, when OPEC promises to flood the market with more supply?”
Crude’s biggest producers and shippers in the Organization of the Petroleum Exporting Countries agreed at a meeting in Vienna to stick to a policy of unconstrained output for another six months.
Oil prices rose right after the decision, as market bulls tried to make up for losses since Wednesday. Brent and U.S. crude fell nearly 3 percent a day in those previous two sessions as traders locked in advance bets that OPEC would not cut supply.
But the dollar’s surge on a stronger-than-expected U.S. jobs report for May pushed crude down more than $1 a barrel. Brent hit seven-week lows, descending into sharp volatility until the late rally.
“The jobs report just blew away expectations and set the dollar on an unexpected run that tore into oil’s gains,” said Phil Flynn, analyst at the Price Futures Group in Chicago.
“But at the same time, bulls were already hedged for the OPEC decision not to cut output and ready for a relief rally after the losses of the past two days.”
Brent settled up $1.28, or 2.1 percent, at $63.31 a barrel, after hitting the April 16 low of $60.94. For the week, it fell 3.6 percent.
U.S. crude jumped $1.13, or almost 2 percent, to settle at $59.13. It lost 2 percent on the week.
The discount, or so-called “contango,” between U.S. crude’s front-month and second-month CLc1-CLc2 widened to its largest in a week as oversupply worries mounted after the OPEC decision.
“To me, this is really what people should be watching as the wider the contango gets, the weaker price will be going forth,” Zahir said.
Data also showed U.S. oil drillers boosted activity in four key shale basins this week despite an overall decline in oil rigs. (Additional reporting by Vladimir Soldatkin in London and Henning Gloystein in Singapore; Editing by Andre Grenon; and Peter Galloway)