US crude inventories fell by three million barrels to 430.6 million barrels up to June 15, according to an American Petroleum Institute report on Tuesday.
Falling production in Venezuela and Libya, as well as the risk of lower output from Iran as a result of United States sanctions, have all increased market worries of a supply shortage.
Regional rival Iran however is fiercely opposed to unwinding the agreed production curbs, as its oil industry is bracing for fresh sanctions following US President Donald Trump's decision to quit the global nuclear pact.
OPEC has reached an agreement in principle to boost oil production, achieving a last-minute compromise that overcame Iran's threats to veto any supply hike.
The most recent price rally followed an OPEC decision to restrict supply in an effort to drain global inventories.
Iran is understood to want a coded critique of the United States, which recently ended an worldwide nuclear agreement with Iran, in the final Opec agreement on Friday.
"We want to prevent the shortage and the squeeze that we saw in 2007-2008", Falih said.
OPEC, together with other key producers including Russian Federation, started withholding output in 2017 to prop up prices, but a tightening market has led to calls by consumers for more supplies.
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Crude oil prices are trading lower early Thursday, but inside yesterday's range.
The market is contending with exactly how much output will change.
"It would seem that an aggregate increase in production for OPEC+ of between 500,000 bpd and 1 million bpd is the range that is being considered", Tchilinguirian said.
Oman's oil minister Mohammed bin Hamad Al-Rumhy said he believed Iran would agree to an output increase on Friday.
OPEC sources also said Iran had demanded that USA sanctions be mentioned in the group's post-meeting communique.
"If China's import demand dries up, more than 300,000 bpd of USA crude will have to find a new destination", energy consultancy FGE said.
The deal looked to be in line with many analysts' forecasts.
"Allocating to Saudi Arabia part of the quota of countries that cannot increase output could be a technical solution, but may not be a political one", Al-Falih said.
If Iran continues to oppose a deal when ministers formally gather on Friday and musters the support of others - perhaps Venezuela, Iraq and Algeria - OPEC may be unable even to issue a communique, let alone decide to increase production.
"This puts Saudi Arabia in a tough position, as unanimity is needed for any accord to be reached", it added.