Brent North Sea crude for delivery in November jumped $1.11 to $105.08 a barrel in London midday deals. Earlier Monday, the contract slid more than two dollars to a one-month low point of $101.66.
New York's main contract, West Texas Intermediate (WTI) for November, gained 59 cents to $80.44.
Prices fluctuated in line with global stock markets, which started the day with big losses before rebounding strongly on reports that an ambitious eurozone debt rescue plan was taking shape and would offer more aid to European banks.
The oil market was meanwhile studying the outlook for energy demand given the economic uncertainty.
"Global oil demand growth has slowed from the high base of last year but still remains healthy on historical standards," Barclays Capital analyst Roxana Mohammadian-Molina said on Monday.
"However, should global growth continue to contract, demand could be scaled back by a big chunk."
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