Speaking at the World Economic Forum at the Swiss ski resort of Davos, Khalid al-Falih said producers have gone "extra miles" and the majority have exceeded their agreed cuts.
He said there's a "very high level of data available" showing the first part of January has shown higher compliance. Earlier today, the International Energy Agency said global oil output is dropping.
However, the IEA's executive director, Fatih Birol, said the higher oil prices prompted by the production cut could see a rise in output from US shale gas producers.
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