By Devika Krishna Kumar

NEW YORK (Reuters) - Oil prices rallied on Wednesday after U.S. crude inventories fell in the most recent week, but gains were capped by worries over the economic fallout from the coronavirus pandemic and weak refining margins.

Oil futures have staged a recovery from recent weakness as production has declined more swiftly than expected, reducing the supply glut that caused storage to fill.

Brent crude <LCoc1> settled up $1.10, or 3.2%, at $35.75 per barrel while July U.S. crude futures <CLc1> ended up $1.53, or 4.8%, at $33.49.

U.S. crude inventories fell by 5 million barrels last week, Energy Information Administration data showed, while stocks at the Cushing, Oklahoma, delivery hub dropped by 5.6 million barrels. [EIA/S]

"What this report confirms is that your worst nightmare - that we're going to run out of storage space - is probably not going to happen," said Phil Flynn, senior analyst at Price Futures Group.

"We need to see more signs that rebalancing is taking place, primarily through more demand," said Gene McGillian, director of market research at Tradition Energy.

Continental Resources <CLR.N>, one of the largest U.S. shale oil producers, on Wednesday urged North Dakota energy regulators to intervene in the oil market through steps including limiting output.

Production in North Dakota has already fallen more than half a million barrels per day (bpd) and has, along with cuts in Texas and elsewhere, helped support prices.

Fuel demand has grown as lockdown curbs have eased worldwide, and shipping data shows the Organization of the Petroleum Exporting Countries and allies are complying with their pledge to cut 9.7 million barrels per day in supply.

U.S. gasoline and distillate inventories rose last week, data showed, as demand slipped. Weak crude refining profits could delay a recovery in demand.

Lingering concerns about the economic fallout from the coronavirus pandemic, especially in the United States, the world's biggest oil consumer, limited gains.

Federal Reserve policymakers repeated a vow to do what it takes to shore up the U.S. economy, minutes from the U.S. central bank's April 28-29 policy meeting released on Wednesday showed.

Unless there is a major event such as a new OPEC decision, extended cuts or new lockdowns, prices are likely to stay around current levels, said Paola Rodriguez Masiu, senior oil markets analyst at Rystad Energy.

(Additional reporting by Laila Kearney, Jessica Resnick-Ault, Ahmad Ghaddar, Jane Chung; Editing by Richard Chang, Marguerita Choy and Paul Simao)