U.S. West Texas Intermediate (WTI) crude futures were at $69.81 per barrel at 0047 GMT, up 56 cents, or 0.8 percent, from their last settlement.
The IEA also said that higher output from OPEC managed to more than offset seasonal declines from non-OPEC members.
Demand for oil grew more slowly in the second quarter but will continue to rise this year and in 2019, the group said.
Oil production by OPEC's defacto leader, Saudi Arabia, has ticked up since May, when it and Russian Federation signaled they could increase output to fill any supply shortages due to upcoming US sanctions on Iran.
Following crippling sanctions on Iran following the collapse of the Washington and Tehran's nuclear deal, the price of a barrel of U.S. crude oil could result in a price rise of $4 (£3.12) a gallon of unleaded fuel at petrol station pumps.
"We are dealing with two issues separately and our stand has been communicated to the USA", added the official on being questioned to whether higher American oil imports could mean replacing Iranian crude.
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U.S. crude stocks fell by 8.6 million barrels in the week to September 7 to 395.9 million, the American Petroleum Institute (API) said on Tuesday, while the U.S. Energy Information Administration (EIA) cut its forecast for U.S. crude output growth in 2019.
Still, fears over a supply crunch remained, with Iran's output slumping by 150,000 barrels last month, according to Opec's monthly market report.
Novak said global oil markets were "fragile" due to geopolitical risks and supply disruptions.
Oil product stocks did rise, with distillate holdings, which include diesel and heating oil, climbing by 6.2 million barrels, while those for gasoline rose 1.3 million, according to the EIA data.
"We are entering a very crucial period for the oil market". The U.S. Treasury department in conjunction with the United International locations on Wednesday imposed sanctions on a number one Libyan militia chief for his attacks on necessary oil facilities in June.
Opec, the Organization of the Petroleum Exporting Countries that accounts for 40% of global production, cut its forecast for oil demand growth next year in its monthly report.
OPEC said the world will need 32.05 million bpd from its 15 members in 2019, unchanged from last month.