Oil firmed to $72 a barrel on Thursday after the International Energy Agency raised its estimate for 2009 oil demand, adding to signs the fall in consumption may have bottomed out.

World oil demand will contract by less than previously expected this year, the International Energy Agency (IEA) said as it raised its 2009 forecast for the first time since August 2008.

Olivier Jakob, oil analyst at Petromatrix, said markets were now in a phase of identifying green shoots of economic recovery. The IEA report will likely be taken as an additional green shoot, he said.

U.S. crude rose 66 cents to $71.99 a barrel by 1337 GMT (9:37 a.m. EDT), a near eight-month high. Brent crude gained 48 cents to $71.28.

Falling inventories in top oil consumer the United States also supported prices.

U.S. crude stocks fell by a sharp 4.4 million barrels last week, against expectations for a modest draw of 400,000 barrels, while products inventories also dropped, the Energy Information Administration (EIA) reported on Wednesday.

Gasoline inventories fell 1.6 million barrels last week against forecasts for a 800,000-barrel build as gasoline demand rose by 0.4 percent over the four-week period, the start of the U.S. summer driving season, the EIA said.

Distillate stocks, including diesel and heating oil, fell by 300,000 barrels, versus analysts expectations for a 1.4 million barrel increase.

Data from China, the second-largest oil consumer, suggested rising demand.

China's crude imports in May rose 5.5 percent from a year ago, the second-highest volume on record, the General Administration of Customs said on Thursday.

The U.S. dollar fell again against a basket of currencies on Thursday, adding support to dollar-denominated commodities.

(Additional reporting by Joe Brock; Editing by James Jukwey))