U.S. light, sweet crude rose $1.41 to $96.50 a barrel by 2:20 ET, while London Brent crude rose $1.86 to $96.25.
Traders said Tuesday's gains were tied to worries about sliding inventories of oil in the United States, where stockpiles have already plumbed a three-year low.
A report from the government due Wednesday morning is expected to show an eighth consecutive decline in crude stocks last week, due in part to export disruptions from key supplier Mexico, according to a Reuters poll.
Adding support Tuesday, armed groups in Nigeria's oil producing south are building up arms and supplies for a major attack on an oil facility, militant and security sources said.
Militant attacks in the No. 8 oil exporter have already slashed the country's exports 20 percent below capacity.
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Oil received some further support after an OPEC delegate told Reuters the exporter group was unlikely to change oil output policy at its upcoming meeting on Feb. 1 if prices stayed close to their current level.
"If the price stays at this level, I don't think they will do anything," the delegate said. "Ministers will be looking at the second quarter when demand declines seasonally."
Oil has fallen since prices crossed the $100 mark for the first time last week, weighed down by fears of a recession in the United States.
A report last week showed the nation's unemployment rate rose to 5 percent in December, its highest in more than two years.
"The biggest concern in the market now is the possibility of a recession in the U.S.," said Tony Nunan, a manager at Mitsubishi Corp's risk management unit.
"Right now, there seems to be a 50-50 chance that it would happen and even if it doesn't, the fear that it might is enough to spook the market."