* Libya output rises to 350,000 bpd after El Sharara oilfield restart
* OPEC world oil market share to shrink in 2015 for 3rd straight year
(Adds quotes, updates prices)
SINGAPORE, July 11 (Reuters) - Oil prices were heading for their third straight weekly loss on Friday as worries about supply disruptions in the Middle East and North Africa eased, although Brent stayed comfortably above $108 a barrel.
Brent and U.S. crude prices had recovered in the previous session, ending their longest streak of daily losses in years. But Brent had dropped 9 cents to $108.58 a barrel by 0620 GMT on Friday, while U.S. crude fell 21 cents to $102.72.
"The premium on crude oil is coming off a bit. Market nervousness about the Middle East is dissipating and traders aren't as nervous as they were a week ago," said Ben Le Brun, a market analyst at OptionsXpress in Sydney.
Supply concerns eased in the Middle East and Africa despite geopolitical tensions in Iraq, Libya and Gaza.
"The market is looking for the bottom line now, after the shock. Things are improving (in Libya and Iraq) and the markets have resurfaced from there," said Tetsu Emori, a commodity fund manager at Astmax Co. Ltd. in Tokyo.
Libya's southern El Sharara field is boosting production and has pushed the country's oil output to 350,000 barrels per day, a spokesman for National Oil Corp said on Thursday.
Analysts warned, however, that it would take months to ramp up production and more unrest is possible.
"We still should be careful and continue watching the market. We don't know when the next supply disruptions in Libya and Iraq will be," Emori said.
In Iraq, exports from southern Basra ports continued despite an ongoing Islamic insurgency.
Sunni militants battling forces loyal to Iraqi Prime Minister Nuri al-Maliki broke into a military base in Diyala province northeast of Baghdad on Thursday, a security source and a local official said.
Meanwhile, investors are looking ahead to second quarter GDP data from China next week to assess fuel demand outlook at the world's second largest consumer.
"We'll focus on the Chinese data next week and that will be a clearer indication of where prices will be going," Le Brun said.
Beijing could implement more stimulus measures to support growth which would lift its oil demand. Chinese crude imports rose 10 percent in the first half this year although analysts attributed the rise to stockpiling.
In the United States, the Energy Department said it would have its planned gasoline stockpile for the Northeast region in place in time to respond to possible supply disruptions at the height of the 2014 hurricane season.
(Reporting by Florence Tan; Editing by Joseph Radford and Michael Perry)