Crude-oil futures moved in a narrow price range in early Asian trade Monday, with gains capped by worries about a recovery in U.S. shale-oil production and as OPEC’s meeting draws closer.

On the New York Mercantile Exchange, light, sweet crude futures for delivery in June traded at $59.77 a barrel at 0252 GMT, up $0.08 in the Globex electronic session. July Brent crude on London’s ICE Futures exchange rose $0.09 to $66.90 a barrel.

Nymex crude ended 0.5% higher last week and has been up for three consecutive weeks, while Brent crude gained 1% last week and has been up for seven of the past nine weeks.

Oil-price gains were capped due to some weak U.S. economic data from Friday and on worries U.S. shale production could recover quickly if prices kept on rising. Last week’s Baker Hughes U.S. drilling rig-count also lost momentum, falling by 8 rigs to 660 rigs, the smallest fall in 23 weeks.

“Reports suggest certain shale formations (such as Eagle Ford and Bakken) are starting to add rigs, which is further weighing on sentiment,” ANZ Bank said.

Many investors are also sticking to the sidelines ahead of the meeting of the Organization of the Petroleum Exporting Countries scheduled for June 5. While most market observers don’t expect a major change in OPEC policy, the meeting might provide more cues on key issues like Iran’s oil-export plans, a Singapore-based trader said.

Morgan Stanley said U.S. oil producers are also cautious about the timing or pricing of resuming oil production levels due to the coming OPEC meeting and the need for some price stability in the market.

But U.S. oil producers are indicating that “$65 may be the new $85,” as break-even costs of oil production have fallen markedly due to new drilling techniques and cost efficiencies, Morgan Stanley’s Adam Longson said.

Mr. Longson also said the Middle East appears to be best positioned for raising oil production, and activity levels remain high in the region, reinforcing concerns about OPEC production levels. “The opportunities in the Middle East, particularly in Saudi and Kuwait appeared to be most favorable given the ease of extraction and political will,” he said.

Nymex reformulated gasoline blendstock for June–the benchmark gasoline contract–rose 26 points to $2.0594 a gallon, while June diesel traded at $2.0073, 25 points higher.

ICE gasoil for June changed hands at $613.75 a metric ton, up $2.75 from Friday’s settlement.