Investors are also turning their focus to Sunday's OPEC meeting with allies for clues on whether the group will boost output again after President Donald Trump called on the cartel to rein in prices. Given the Kingdom's preference for Brent prices above $80/barrel, OPEC may not increase supply unless prices remain elevated.
US West Texas Intermediate crude was up 55 cents, or 0.8 per cent, at $71.67 a barrel, after rising almost 2 per cent the previous session. On Wednesday, WTI climbed back above $70 a barrel.
One glaring absence from the Algiers proceedings will be Iranian oil minister Bijan Zanganeh, who has railed against Saudi Arabia and Russian Federation increasing production as Iran's market share is threatened. After starting the year around $60 a barrel, U.S. oil prices raced above $74 this summer.
OPEC and its allies seem poised for another contentious meeting in Algeria this weekend as Iran - wounded by USA sanctions - cries betrayal and threatens to veto decisions.
Trump sent several tweets stating that prices are too high after Brent rose to a three-year high in May.
U.S. sanctions on Iran's oil exports come into force in November, with supply from the country already at two-year lows.
Crude inventories fell 2.1 million barrels last week to 394.1 million barrels, the lowest level since February 2015, EIA data showed. The last time the United States led the world in oil production was 1973. The agency forecasts an average of 10.7 million barrels per day for 2018, compared with 9.4 million barrels per day a year ago, and forecasts an average of 11.5 million barrels per day in 2019.
U.S. sanctions on Iran's oil exports come into force on 4 November and many buyers have already scaled back Iranian purchases.
"The OPEC Monopoly must remember that gas prices are up & they are doing little to help", he tweeted on July 5.
Consultancy JBC Energy said in a note "The market may have taken this as a sign that supplies may not go up much in response to further declines in Iranian crude exports". The United States relies on those tankers for its oil imports.
But while prices have risen, they are nowhere near the historic high of $143 per barrel in June 2008.
Under pressure from the US president, the Organization of the Petroleum Exporting Countries, Russia and other allies agreed in June to boost production by 1 million barrels per day, having participated in a supply-cutting deal since 2017.