* Brent, WTI gain for sixth week
* Brent has risen 19% this week, WTI up 11%
* OPEC+ to meet Saturday to discuss output cuts - Russia
* U.S. Gulf offshore fields in path of Storm Cristobal
(Adds weekly change, settlement prices, storm Cristobal update)
By Jessica Resnick-Ault
NEW YORK, June 5 (Reuters) - Oil prices rose on Friday after an unexpected fall in the May U.S. jobless rate and OPEC's decision to bring forward to Saturday discussions on whether to extend record production cuts.
Brent crude LCOc1 futures settled up $2.31, or 5.8%, at $42.30 a barrel, surging 19.2% on the week. U.S. West Texas Intermediate (WTI) crude CLc1 futures rose $2.14, or 5.7%, to $39.55 a barrel, rising 10.7% on the week.
The U.S. Labor Department reported a surprise fall in the jobless rate to 13.3% last month from 14.7% in April.
Brent has risen 17% since May 29 to reach a three-month high, in a range more comfortable for producers like Russia. The contract has more than doubled since crashing as low as $15.98 a barrel on April 22. WTI is up 11%.
Both benchmarks were headed for a sixth week of gains, lifted by the output cuts and signs of improving fuel demand as countries ease lockdowns imposed to fight the new coronavirus outbreak.
"OPEC and the U.S. jobless drop boosted the market," said Phil Flynn, senior analyst at Price Futures Group in Chicago. "If we see jet fuel demand recover, that may give us hope that we can look ahead to a day where these supplies can dwindle down," said Flynn, pointing to American Airlines (NASDAQ: AAL ) Group Inc's announcement Thursday about increased U.S. flights in July. energy ministry said a video conference of a group of leading oil producers, known as OPEC+, would be held on Saturday. market was hopeful that some laggard countries may have agreed to align with the production cut deal.
OPEC+ had said it would bring forward the meeting, which had been scheduled for next week, should Iraq and others agree to boost adherence to supply cuts. OPEC+ sources said Saudi Arabia and Russia had agreed to extend deeper cuts until the end of July but said Riyadh was also pushing to extend them until the end of August.
If OPEC+ fails to agree to roll over the output curbs, the cut could drop back to 7.7 million bpd from July through December as previously agreed.
Adding support was Tropical Storm Cristobal. It is expected to enter the central Gulf of Mexico, an area rich with offshore platforms, and could make landfall along Louisiana's refinery row on Sunday.
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