Brent crude futures, the global benchmark for oil prices, were at $73.05 per barrel at 0036 GMT, down 39 cents, or 0.5 percent, from their last close.
As recently as April, Saudi Energy Minister Khaled al-Faleh had voiced support for the oil cut deal, saying the market had the capacity to absorb higher prices.
The historic 24-nation pact has succeeded in its goals of balancing oil markets and lifting crude prices, and the two biggest producers want a relaxation of quotas as soon as next month. Oil prices climbed above $80 last month after the United States withdrew from the nuclear deal with Iran.
The move would effectively wipe out existing production cuts of 1.8 million bpd, which have helped rebalance the market in the past 18 months and lifted oil prices to almost $80 per barrel from as low as $27 in 2016. Russia, by far the largest non-member to join OPEC's cuts agreement, has said it would be happy with lower crude prices and appears keen to start up new fields.
Expressing his optimism over regaining balance to the worldwide oil market, Al Mazrouei said: "Looking ahead, I remain optimistic that we will fulfil our goal of delivering sustainable oil market stability, which is meant to serve the long term interests of producers, consumers and the global economy".
Crude inventories fell 3 million barrels in the week to June 15 to 430.6 million, compared with analysts' expectations for a decrease of 1.9 million barrels. Those who hate me call me crude."I worry for my future; everyone now talks down on me".
Traders also reacted to reports that China could be planning to implement tariffs on US crude oil. With potential 1 million barrels/day addition by OPEC, the market looks to be well supplied until next year.More news: Time trumps Trump again: Pulitzer Prize-winning John
Greg McKenna, chief market strategist at futures brokerage AxiTrader said there would likely be oil price volatility in the week ahead of the meeting.
For tanker owners, there is much at stake on 22 June when OPEC oil ministers gather in Vienna for what is likely to be a particularly bad-tempered meeting. It isn't yet a done deal, as Iran is opposed to increasing production and Brent futures recovered after reports of a much smaller compromise output hike.
OPEC's de facto leader, Saudi Arabia, and non-member Russian Federation have proposed gradually relaxing production cuts - in place since the start of 2017 - while OPEC members Iran, Iraq, Venezuela and Algeria have opposed such a move.
For Opec, the next move will be to consider to return to a compliance ratio of 100 per cent of the agreed production cuts of 1.8 million barrels per day in 2016. The excess is mostly driven by the collapse in crude oil production in Venezuela.
Two OPEC sources told Reuters that even Saudi Arabia's Gulf allies Kuwait and Oman were against big, immediate increases in output. Output in Saudi Arabia jumped by 85,500 barrels a day, but was partly offset by production outages in Nigeria, Venezuela and Libya.
In an escalating spat over the United States' trade deficit with most of its major trading partners, including China, US President Donald Trump said last week he was pushing ahead with hefty tariffs on US$50 billion of Chinese imports, starting on July 6.
The market was decidedly less rosy overnight - prompt Brent traded as low as $72.45/b - as tensions between the U.S. and China escalated.