* Brent and U.S. crude down more than 5% for week
* U.S. job growth increased moderately in September
* Supply concerns fade with restored Saudi output
* Coming up: Baker Hughes rig count data at 1 p.m. ET (New throughout, updates prices, market activity and comments; new byline, changes dateline, previous LONDON)
By Stephanie Kelly
NEW YORK, Oct 4 (Reuters) - Oil prices rose on Friday as an increase in U.S. jobs eased some financial market concerns that a slowing global economy could dent oil demand, but crude remained down more than 5% for the week, on track for a second consecutive weekly decline.
Brent crude futures rose 71 cents, or 1.2%, to $58.42 a barrel by 11:30 a.m. EDT (1530 GMT). West Texas Intermediate (WTI) crude futures rose 36 cents, or 0.7%, to $52.81 a barrel.
Still, both benchmarks were on track to fall about 5.6% for the week, their biggest weekly losses since July.
"The oil market is fixated on macro-economic issues and not necessarily current supply or demand," said Phil Flynn, an analyst with Price Futures Group in Chicago.
U.S. job growth increased moderately in September, with the unemployment rate dropping to near a 50-year low of 3.5%, according to a U.S. Labor Department report.
The report, however, came on the heels of a string of weak economic reports, including a plunge in manufacturing activity to more than a 10-year low in September and a sharp slowdown in services industry growth to levels last seen in 2016.
"The crisis in the manufacturing sector now appears to be spilling over to the previously robust services sector. This is not good news for oil demand. After all, this also reduces the demand for transport," said Carsten Fritsch, senior commodity analyst at Commerzbank.
On the supply side, Saudi Arabia's energy minister, Prince Abdulaziz bin Salman, said on Thursday the world's top crude oil exporter had fully restored oil output after attacks on its facilities last month knocked out more than 5% of global oil supply.
"That Saudi restored its production back to original capacity sooner than expected means investors had to price out raised supply risks at a faster clip than would have otherwise been the case," said Fawad Razaqzada, market analyst at futures brokerage Forex.com.
Razaqzada said weak economic data, particularly from the U.S. manufacturing sector, also raised fears for oil demand, "but now that some of these factors have been priced in, oil prices may fall less sharply going forward or at best start to form a base."
Investors are also watching for further developments on tensions between the United States and Iran.
France said Iran and the United States have one month to get to the negotiating table, suggesting that Tehran's plan to increase its nuclear activities in November would spark renewed tension in the region.
In an indication for future production, U.S. rig count data is due to be released at 1 p.m. EDT on Friday.
Additional reporting by Bozorgmehr Sharafedin in London and Roslan Khasawneh in Singapore; Editing by David Goodman, David Evans and David Gregorio