By Laura Sanicola

(Reuters) - Oil prices settled sharply higher on Thursday, rebounding from steep losses the previous two sessions, as investors returned their focus to tight supply despite nagging fears of a potential global recession.

Brent crude futures were up $3.96, or 3.9%, at $104.65 a barrel. U.S. WTI crude futures climbed $4.20, or 4.3%, to $102.73 a barrel.

Trade was volatile. At session lows, prices were down about $2.

Wall Street's main indexes opened higher, making up for some losses last week tied to recession fears as central banks aggressively hike interest rates to fight inflation.

"With Russian oil supplies set to drop as the year progresses and it runs out of Western parts to maintain fields, and with the rest of OPEC hopelessly uninvested in maintaining production capacity, I fear the days of $100 oil will be with us for some time yet," said Jeffrey Halley, a senior market analyst at OANDA.

On the supply side, traders are bracing for oil supply disruptions at the Caspian Pipeline Consortium (CPC), which has been told by a Russian court to suspend activity for 30 days.

Exports via the CPC, which handles about 1% of global oil supplies, were still flowing as of Wednesday morning.

Further squeezing global supplies, Washington tightened sanctions on OPEC member Iran on Wednesday, pressuring Tehran as it seeks to revive a 2015 Iran nuclear deal and unleash its exports.

Oil prices have dropped in the past few weeks as investors worried that a sharp economic slowdown could slam demand for commodities.

"Margin call selling that appeared to spur much of this week’s price plunge has likely been completed," said Jim Ritterbusch, president of Ritterbusch and Associates LLC in Galena, Illinois.

U.S. crude oil stockpiles rose by 8.2 million barrels last week, driven by an increase in inventories and as refiners cut output, the Energy Information Administration said.

However, product supplied, the best proxy for U.S. consumer demand, was up in the latest week to 20.5 million bpd.

"Almost every indicator in that report seems to suggest that just demand is gaining momentum," said Phil Flynn, an analyst at Price Futures group.

On Wednesday, Brent and WTI settled at their lowest since April 11. On Tuesday, WTI slid 8% while Brent tumbled 9% - a $10.73 drop that was the third biggest for the contract since it started trading in 1988.

"Recession fears continue to grow and that obviously does raise some concerns for the demand outlook," said Warren Patterson, ING's head of commodity research.