The group has been forced to take a softly-softly approach to oil production increases after cracks emerged within the cartel and threatened to dash the chances of a deal.
The price of oil jumped after the announcement, with the worldwide benchmark, Brent, gaining $1.61 to $74.66 a barrel.
While Saudi Arabia's cutting by more than required has helped Opec's compliance, involuntary reductions in Venezuela amid economic crisis and in Angola due to natural decline have had a larger impact and can not be reversed at short notice.
The Saudi push is viewed as a bid to appease the United States which is on course to reimpose sanctions on the Islamic Republic, including on its oil sales.
But the real increase will be smaller because several countries that recently underproduced oil will struggle to return to full quotas while other producers will not be allowed to fill the gap.
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That would effectively mean a boost from other oil producing nations such as Saudi Arabia, that has voluntarily cut more deeply than planned.
The world faces likely lower oil exports from Iran, Opec's third-biggest producer, after US President Donald Trump pulled out of a 2015 nuclear accord with a vow to renew sanctions against Tehran.
Falling production in Venezuela and Libya, as well as the risk of lower output from Iran as a result of U.S. sanctions, have all increased market worries of a supply shortage.
Going into the meeting, Saudi Arabia and Russian Federation are in favor of raising output.
That reflects a one million barrel-a-day adjustment on paper to the production cuts implemented by the Organisation of Petroleum Exporting Countries and its allies, the delegate said, asking not to be named because the information is private.
The problem for traders and ministers trying to estimate the price needed to rebalance the market is that consumption responds to price changes with a delay of six to 18 months.
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OPEC did not say which of its members would supply the additional crude, which should start to flow into the market in July.
"There isn't a lot of spare capacity in the world". If we lose a million bpd of output from Venezuela and Iran in the fourth quarter, where will all these barrels come from?
"We could see this knocking $5 per barrel off Brent", Allardyce said.
'We want to prevent the shortage and the squeeze that we saw in 2007-2008, ' Falih said, referring to a time when oil rallied close to $150 per barrel.
But production has dipped more than expected thanks to factors including outages in Venezuela.
"As a group we can meet the 100 percent compliance. OPEC is not part of the Department of Energy of the United States", RFE/RL cited the minister as saying.
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Iraq is advocating a postponement of the decision on output for three months, but, according to the country's Oil Minister, Jabbar al-Luaibi, the committee would not agree to it. Venezuela also objected to the recommendation.