By Amrith Ramkumar

Oil prices inched higher Wednesday, continuing a recent rebound after data showed U.S. crude stockpiles fell more than anticipated last week.

U.S. crude futures for August delivery were recently up 0.9% at $39.62 a barrel. Prices are near their highest level since early March, buoyed by recovering fuel demand and supply cuts by the Organization of the Petroleum Exporting Countries and allies including Russia.

Sliding U.S. crude output is also supporting the rally. On Tuesday, prices closed out their best quarter since 1990.

Wednesday's data showed inventories fell 7.2 million barrels last week, a much bigger drop than the 100,000-barrel decline expected by traders and analysts surveyed by The Wall Street Journal.

Still, stockpiles remain elevated after surging earlier in the year, and many analysts are concerned about a recent rise in coronavirus cases in key fuel-consuming states such as Texas, Florida and California. Recent data have indicated that the global economic recovery and rebound in oil consumption could be slowing down, a concerning development for bullish crude investors counting on surging demand.

At the same time, strong compliance from OPEC producers with recent supply cuts and indications that the cartel could act carefully in bringing back output continue to keep crude in its current trading range.

"Although there is still the danger of demand outages in view of increased new cases of Covid-19, OPEC+ seems to have the market under control at the moment," Commerzbank analysts said in a note.

Brent crude futures for September delivery, the global gauge of oil prices, added 1.4% to $41.83 a barrel on the Intercontinental Exchange Wednesday.

Traders are closely watching to see if OPEC producers and U.S. companies start bringing back output in response to higher prices. U.S. crude supply held steady at 11 million barrels a day last week, up from a recent low of 10.5 million barrels a day but well below an early year record of 13.1 million barrels a day, Wednesday's figures showed.

Investors were also weighing an announcement from Pfizer Inc. and BioNTech SE of positive early stage results in a human clinical trial for a coronavirus vaccine. The news helped lift stocks and crude prices. Optimism about vaccine development has buoyed stocks and oil in recent weeks, with investors hoping that eventual completion of a vaccine would support consumer confidence and the global economy.

Elsewhere in commodities, most actively traded gold futures fell 1.4% to $1,774.60 a troy ounce, paring some of their recent gains. The haven metal hit a nearly nine-year high above $1,800 on Tuesday and has surged lately with economic uncertainty and ultralow interest rates boosting demand.

Write to Amrith Ramkumar at amrith.ramkumar@wsj.com