Crude closes at $56.71/barrel, up 32 cents or 0.57%

U.S. crude settled up 32 cents at $56.71 per barrel on Thursday on news that a tribal group made up of former Al Qaeda militants took control of a major southern oil terminal in Yemen after military forces protecting it withdrew from the site.

The terminal is one of the major hubs for the Hadramout region exporting an average of 120,000 to 140,000 barrels per day of crude from fields in the area.

Read MoreOPEC: Rivals' oil supply growth will slow

Brent crude futures for June traded up 73 cents at $64.05 a barrel by 2:26 p.m. EDT on Thursday, after touching a front-month Brent 2015 peak. WTI also traded above $57 per barrel for the first time since December earlier in the session.

Benchmark contracts fell earlier on Thursday after OPEC reported its oil output surged in March, adding to excess supply in the market despite more evidence that its strategy of letting prices fall to hurt other drillers is taking effect.

Crunch time for drillers
Crunch time for drillers   

In a monthly report on Thursday, OPEC said demand for its oil this year would be 80,000 barrels per day higher than previously thought as lower prices curb supplies in the United States and other non-member countries.

But the report also confirmed industry estimates of a surge in OPEC production in March, which jumped by 810,000 bpd led by higher output in Saudi Arabia and Iraq and a partial recovery in Libyan production.

Read MoreOil demand seen rising, but Iran calls for cut

U.S. crude has been logging its strongest upswing this year as ebbing fears of an inventory overflow and renewed hedging in far-distance futures flatten the forward curve.

"We turn extremely bullish on oil," Singapore-based energy brokerage Phillips Futures said in a note to clients. "This whole rally was primarily due to drops in U.S. crude production. We see the four-week average for crude production turning negative for the first time since July '14."

Oil prices collapsed in the six months to January, pushing Brent down more than 60 percent to almost $45 a barrel.

But the market has gradually recovered this year as much lower prices have discouraged oil exploration and production, especially in the United States.

"People are realizing that the U.S. production juggernaut is slowing, at least for now," said Virendra Chauhan, oil analyst at London-based consultancy Energy Aspects. "U.S. production is down for the second time in three weeks and refinery runs are spiking up, driving demand higher."

Reuters technical analyst Wang Tao told Reuters Global Oil Forum that Brent could rise toward $70 a barrel in the near term, but that a sharp downturn could happen after that.

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U.S. oil prices jumped on Wednesday after U.S. inventories built up more slowly than expected, although still to a new record. Talks between major oil producers also triggered speculation of production cuts, even though most analysts said these were unlikely.

Despite the oil price rally, the market remains oversupplied, analysts say.

"The recent bounce comes despite a surge in OPEC crude oil production in March which is likely to have been sustained in April," ANZ bank said.