Oil prices rose sharply in the spring as production collapsed in crisis-ridden Venezuela and traders anticipated Trump's withdrawal of the United States from the Iran nuclear deal.
OPEC agreed with Russian Federation and other oil-producing allies this month to raise output from July by about 1 million bpd.
US President Donald Trump said on Saturday that Saudi Arabia's King Salman had agreed to his request to increase oil production "maybe up to 2,000,000 barrels", an extraordinary amount not confirmed by the kingdom and which would push the OPEC leader to a level of production never tested before.
Saudi authorities had no immediate comment.
On 20 April he tweeted that oil prices were "artificially very high", saying this was "no good" and "will not be accepted!"
Though the OPEC didn't disclose country quotas in the recent announcement of 1bpd output hike, Bell sees there are a few countries with available capacity to raise production and any increase in production would be borne most significantly by Saudi Arabia, the UAE and Kuwait.
"Prices to [sic] high!"
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In a statement Saturday, Saudi Arabia said that King Salman had spoken to Trump and that the leaders discussed the need to address any potential shortages in the supply of oil as well as maintain stability in the oil markets.
USA officials are pressing allies in Europe, Asia and the Middle East to adhere to the sanctions once they are re-imposed, with the aim of pressuring Iran into negotiating a new agreement. Average prices for unleaded gas, including taxes, averaged $2.83 a gallon for the week ending June 25 - up about 55 cents over the same period past year.
"We will be in uncharted territory".
Trump earlier on the basis of conversations with Salman announced that the king promised him to increase daily oil production by 2 million barrels.
However, Saudi Aramco CEO Amin Nasser told journalists in India on Monday that the state oil company has spare capacity of 2 million barrels of oil a day. The kingdom pumped slightly more than 10 million barrels a day in May.
The statement reported by Saudi media did not mention any intention by Saudi Arabia to raise production by 2 million bpd.
At the OPEC meeting last week, Iran's oil minister said that the cartel should not be influenced by Trump and should deal with supply and demand. At meetings in Vienna on 22-23 June, OPEC and its allies cobbled together a delicate accord in order to satisfy some producers, like Iran and Venezuela, which wanted to limit output, and others like the Saudis, which sought to ease away from the supply cuts. In Libya, where a dispute over control of key ports has hindered output, the Arabian Gulf Oil Co. on Saturday halted 220,000 barrels a day of production, according to a person familiar with the outage.