World oil prices soared on Tuesday, mirroring the performance of global equities, as markets followed eurozone debt developments closely. Brent North Sea crude for delivery in November jumped $1.59 to $105.53 a barrel in London midday deals. New York\'s main contract, West Texas Intermediate (WTI) for November, rallied $2.18 to $82.42. \"Oil prices have recovered quite a bit,\" said Commerzbank analyst Carsten Fritsch. \"The main reasons are a change of sentiment on financial markets, reflected in rising equity markets and a somewhat weaker US dollar. \"The downside risks for the economy and oil demand have not disappeared overnight, so a renewed price fall cannot be ruled out,\" he added. Greek Prime Minister George Papandreou was to meet German Chancellor Angela Merkel for talks Tuesday on containing a eurozone debt crisis which US President Barack Obama said is scaring the world. Stock markets around the globe rallied sharply on hopes European leaders would finally get a grip on the long-running crisis threatening the euro project, even if analysts cautioned such euphoria could prove short-lived.