By Scott DiSavino

NEW YORK (Reuters) - Oil were mostly steady on Thursday as rising U.S. fuel inventories and concerns about the impact of surging coronavirus cases on energy demand offset a weaker dollar, which is usually supportive.

Brent futures fell 8 cents, or 0.2%, to $44.21 a barrel by 11:57 a.m. EDT (1557 GMT), while U.S. West Texas Intermediate (WTI) crude rose 12 cents, or 0.3%, to $42.02.

Both benchmarks earlier traded close to four-month highs hit earlier this week.

The U.S. dollar, meanwhile, was trading at its lowest against a basket of currencies <.DXY> since September 2018. A weaker dollar usually spurs buying of dollar-priced commodities, like oil, because they become cheaper for holders of other currencies.

"Genuine price support comes from the weak dollar, which helps physical oil demand," said Tamas Varga of oil brokerage PVM.

But rising U.S. oil inventories and coronavirus cases weighed on prices.

U.S. crude and distillate inventories rose unexpectedly and fuel demand slipped last week, the U.S. Energy Information Administration said on Wednesday, as a sharp rise in coronavirus cases hit U.S. consumption.

U.S. coronavirus cases approached 4 million on Thursday, with more than 2,600 new cases every hour on average - the highest rate in the world, a Reuters tally showed.

"The oil demand outlook should struggle in the short-term as geopolitical tensions put global trade relations at risk and as the coronavirus spread seems to have crippled reopening momentum," said Edward Moya, senior market analyst at OANDA in New York.

Adding to uncertainty in the market, U.S.-China relations deteriorated as Washington gave Beijing 72 hours to close its consulate in Houston after spying allegations.

The Chinese foreign ministry said the U.S. move had "severely harmed" relations and that China would be forced to respond.

(Additional reporting by Ahmad Ghaddar in London, Naveen Thukral and Koustav Samanta in Singapore; Editing by Marguerita Choy and Barbara Lewis)