The Organization of the Petroleum Exporting Countries is meeting in Vienna in an effort to cool the market after oil prices rose to $80 a barrel.
Iran's oil minister walked out of an OPEC meeting to increase the supply of crude. The proposal has yet to win the backing of all OPEC members, and may meet resistance from more hawkish countries in the group including Venezuela and Algeria as well as Iran.
Falling production in Venezuela and Libya, as well as the risk of lower output from Iran as a result of USA sanctions, have all increased market worries of a supply shortage.
"An agreement was reached yesterday to release the equivalent of about 1m barrels to the market; it will be distributed pro rata", Al-Falih said on Friday, of an Opec committee meeting on Thursday.
OPEC takes its decisions by unanimity, so if Iran were to wield its veto Saudi Arabia would be left only with the option of assembling a coalition of willing countries to bypass Tehran's opposition. Oil traded as low as $27 in 2016.
In 2000, then-US President Bill Clinton's energy secretary, Bill Richardson, phoned Ali al-Naimi, the Saudi oil minister at the time, during an Opec meeting to ask for more oil.
Opec has a history of hard meetings as well as clashes between Iran and Saudi Arabia.
Trump's involvement in pressing for OPEC to act - which in addition to his tweets include a behind-the-scenes request for a 1 million-barrel-a-day supply hike - could make it hard for Tehran to accept a compromise.
Brent oil prices were up 1.8% on Friday.
The move infuriated Iran, and Zanganeh refused to sign up to the meeting's decision to raise output.
But a member of Nigerian delegation to the event said as a loyal member, Nigeria will support the position of OPEC leadership to retain the current supply level in order stabilise the market.
Also of concern was the USA immigration crisis after Trump backed off an unpopular hardline policy that had led to children being separated from their parents when they crossed illegally into the United States from Mexico.
Falih said that recent production outages in Venezuela, Libya, and Angola have already reduced global supplies by about 1 million barrels a day.
"OPEC is listening to consumers", Bob Dudley, the chief executive of BP Plc, said on the sidelines of the OPEC conference in Vienna.
"We want to prevent the shortage and the squeeze that we saw in 2007-2008", Falih said.
He acknowledged that a big production hike might be "politically unacceptable" to some OPEC countries and said it was important to be "sensitive" to those concerns.
"Globally, crude prices have gone beyond the threshold, which can be sustained by the world, particularly countries like India, which is a key driver of world economy", Mr. Pradhan said at an OPEC conference in Vienna.
The US, which rivals Russian Federation and Saudi Arabia for the position of world No.1 oil producer, is not participating in the current supply pact.