By 4:37pm EST, the WTI benchmark was trading up 0.27% on the day to $63.90 while Brent was trading up 0.19% on the day at $69.28.
Elsewhere, threats by Nigerian militants on Wednesday to attack offshore oil facilities within days were supportive of prices.
In what seems to be shaping up as the analytical community and media fomenting over a non-issue, crude market gains on Wednesday caused experts to complain that oil prices have reached excess levels and this will only stimulate us output - which in turn will cause the Organization of the Petroleum Exporting Countries (OPEC), who are the masterminds of the gains via its production cutbacks - to abandon its strategy prematurely. WTI Crude oil futures are quoting at $64.23 per barrel, up 0.45% on the day.
Traders said that oil markets were generally well supported by supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russian Federation, who started to withhold production in January a year ago and are expected to continue their restraint through 2018.
The API data also showed a well-supplied fuel product market, which could mean lower crude demand going forward.
"Prices ... rallied on the back of noticeable de-stocking of crude inventories", said Fawad Razaqzada, market analyst at future brokerage Forex.com.
The continued drop in USA crude oil inventories corresponded to a decline in United States production for the week ending January 5, coming in at 9.492 million bpd compared to the week prior of 9.782 million bpd.
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Al-Sabah acknowledged the positive response of the oil market to the implementation of the "Declaration of Cooperation" in 2017, including the unprecedented high levels of conformity with the voluntary production adjustments, with participating countries seeing average monthly conformity levels of more than 100 percent throughout the whole year.
Reuters cited Russian Energy Minister Mr Alexander Novak as saying that a global deal to cut oil output led by OPEC and Russia should continue because the market is still not balanced.
Petrol stocks rose by 1.8-million barrels while distillate fuels stockpiles, which include diesel and heating oil, climbed by 609,000 barrels, the API data showed.
The firm said the reasons for this expected slowdown were an expected rise in US oil output as well as a slowdown in demand growth.
U.S. crude inventories fell by 5.1-million barrels in the week ended January 12 to 411.5-million, according to the American Petroleum Institute on Wednesday.
Despite this, traders said prices were unlikely to fall far due to risks to supply disruptions.