* Record Saudi output, U.S. crude stocks jump * Concern eases of rapid rise in Iranian oil exports (Updates prices, adds comment) By Alex Lawler LONDON, April 10 (Reuters) - Oil edged further below $57 a barrel on Friday, pressured by evidence of ample supplies including the biggest jump in U.S. inventories since 2001 and Saudi Arabian output reaching a record high. The market was still heading for a weekly gain, having rallied on Thursday in response to strong German economic data that lifted the oil demand outlook and easing concern about a rapid rise in Iranian oil supplies. Brent crude had slipped 13 cents to $56.44 a barrel by 0952 GMT, but remained on track for its third weekly gain in four. U.S. crude was down 43 cents at $50.36. "Most of the fundamental factors are still pointing to lower prices," said Eugen Weinberg, analyst at Commerzbank. "At the moment, we have an oversupply of more than 1 million barrels per day." The price of Brent has halved from $115 a barrel in June last year, a drop that deepened after OPEC refused to cut output, choosing to defend market share instead. Top exporter Saudi Arabia was the driving force behind the policy shift. While some OPEC members are urging output cuts to boost prices, Saudi Arabia has shown no sign of a rethink. Oil Minister Ali al-Naimi told reporters on Tuesday Riyadh has boosted its crude production to 10.3 million bpd, the highest rate on record. Further pressuring prices, a U.S. government report on Wednesday said domestic crude stocks surged nearly 11 million barrels last week, the biggest gain in 14 years. A glut of unsold Nigerian crude is building up too, traders say. This is particularly bearish for Brent, because Nigerian crude is priced against it. Some support for crude came from doubts about how fast Iran can resolve a deal over its nuclear programme that would open the way to more oil sales. Iranian Supreme Leader Ayatollah Ali Khamenei on Thursday demanded that all sanctions on Iran be lifted on the same day as any final agreement, while the United States maintains its position that sanctions will only be removed gradually. "Oil sanctions remain very much in place," said Harry Tchilinguirian, head of commodity markets strategy and oil strategy at BNP Paribas. "A significant return of Iranian oil is unlikely before the end of this year, if not next." (Additional reporting by Florence Tan; Editing by Ruth Pitchford and Jason Neely)

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