Brent North Sea crude for September delivery rose by just 13 cents to $57.05 a barrel in midday London trade on the first day of the new contract.
US benchmark West Texas Intermediate for delivery in August fell a marginal three cents to $50.88 per barrel compared with Thursday's close.
Crude investors continue to fret as the global economy struggles to get back up to speed, despite a strong pick-up in the United States, the world's biggest oil consumer.
While fears over the Greek debt crisis abate, prices took a hit this week after crude-rich Iran and world powers agreed a historic deal to check the country's nuclear ambitions, which in turn eases crippling sanctions on its crucial oil exports.
Expectations that Iranian crude would hit an already saturated market spooked dealers, although those worries subsided slightly on the realisation it would not arrive until next year.
"There is a genuine focus back on the glut," Jonathan Barratt, the chief investment officer at Ayers Alliance Securities in Sydney, told Bloomberg News.
"In the absence of solid economic data, it's very hard to see prices going higher."
Adding to the supply worries, the US Energy Information Administration said on Wednesday stockpiles in Cushing, Oklahoma, the delivery point for WTI futures and the biggest oil storage centre in the US - climbed again in the week to July 10.
A rally in the US dollar - after Federal Reserve head Janet Yellen said interest rates would rise by year's end - also kept crude rates tempered.
A strong greenback, at highs not seen since early June, makes dollar-priced oil more expensive for
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