Brent crude, the international benchmark, was trading up 0.47 per cent at $70.86 a barrel at the time of writing after hitting $71.05 earlier today.
The US benchmark, West Texas Intermediate, rose as high as $66.35 a barrel after breaking the $65 a barrel mark yesterday afternoon for the first time in three years.
The Energy Information Administration (EIA) yesterday said US inventories had fallen to 411.6m barrels, the lowest since February 2015. Despite falling less than analysts had expected, oil prices were buoyed by the news.
Mike van Dulken and Henry Croft, analysts at Accendo Markets, said: "Crude oil benchmarks have traded fresh three-year highs overnight as a bullish US EIA inventories drawdown adds further fuel to bullish Opec production cut speculation."
The Organisation of the Petroleum Exporting Countries (Opec) is leading an agreement among members and non-members including Russia to cut oil supply by about 1.8m barrels per day until the end of 2018.
Earlier this week, Saudi Arabia, the cartel's de facto leader, said "cooperation" between Opec and its partners will continue beyond 2018.