LONDON—Oil prices were trading down on Friday ahead of closely watched U.S. oil drilling data.

Brent crude for July delivery recently fell 0.2% to $66.39 a barrel on London's ICE Futures exchange. On the New York Mercantile Exchange, light, sweet crude futures for delivery in July were trading at $60.54 a barrel, down 0.3% from Thursday's settlement.

Investors were focusing on the release of the latest U.S. oil drilling rig count—a proxy for activity in the industry—later on Friday by Baker Hughes Inc.

There are now about 59% fewer rigs working since a peak of 1,609 in October. The rate of decline, however, has slowed in recent weeks and some shale oil companies are expecting to add rigs in the coming months if prices stabilize near the current levels.

"The current price levels may keep some players in business and even entice others to come back," analysts at JBC Energy said in a report. "The first plays to rise from the dead and post further growth could be in the U.S. and. such a turn of events could keep production up and lengthen the global balance further even if prices lose some of their luster."

Oil markets have rebounded in recent weeks to their highest level so far this year on the back of expectations of a slowdown in U.S. output, fresh unrest in the Middle East, signs of stronger demand and a weaker U.S. dollar.

But Barclays warns that oil markets aren't out of the woods yet and oil prices are still 42% below last year's peak levels.

"The rebound off of a low base has been considerable, but oil prices are still well below the 2014 peaks and oil market fundamentals are still weak," Keith Parker, an analyst at Barclays, said.

According to JBC, while oil demand has so far been strong, the global oversupply of crude is far from over and could see more stock building well into next year. Record high oil exports from OPEC members as well as a potential lifting of the Iranian sanctions add to the weaker market outlook, JBC said.

"Putting these factors together, the summer relief hitting the market will be very brief and with all the storage volumes kicking around, there is little reason to get overly bullish. As a result, we see Brent averaging $61 per barrel over the June-August period," JBC said.

Nymex reformulated gasoline blendstock for June—the benchmark gasoline contract—fell 0.1% to $2.0820 a gallon, while ICE gas oil for June changed hands at $605.50 a metric ton, down $3 from Thursday's settlement.

Eric Yep contributed to this article

Write to Georgi Kantchev at georgi.kantchev@wsj.com

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