The price of oil has jumped 55% since OPEC agreed to cut production by 1.8 million bpd.
Oil prices have spiked by as much as 20% this year, in part because OPEC has produced even less than was foreseen under the 2016 agreement, which was supposed to reduce supply by 1.8 million barrels per day.
Zanganeh, speaking to reporters on the sidelines of a Vienna seminar earlier this week, accused Trump of trying to politicize OPEC and said it was USA sanctions on Iran and Venezuela that had helped push up prices.
Iran, Opec's third-largest producer, has so far been the main barrier to a deal as it called on Opec to reject pressure from US President Donald Trump to pump more oil.
As tensions mounted, the Iranian and Saudi ministers huddled for bilateral talks on Friday morning, holding up the start of the closely watched OPEC meeting.
The output gain is nominal. USA investment bank Jefferies said an increase in "the range of 450-750,000 bpd seems the most likely outcome" of the meeting.
The Organization of the Petroleum Exporting Countries and other top crude producers, meeting in Vienna, agreed to raise output from July by about 1 million barrels per day (bpd). Trump has used Twitter to complain about high oil prices - and blame OPEC - twice since April.
Iran's Oil Minister Bijan Namdar Zanganeh walked out that meeting, telling reporters he did not think an agreement could be reached.
Do you think Trump will issue pardons after the Russian Federation probe ends?
Rudy Giuliani speaks at the Iran Freedom Convention for Human Rights and democracy in Washington, May 5, 2018. But Trump has seized on the report as fodder for his decision to fire Comey last May.
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.
More important to Saudi Arabia than extra petrodollars is containing Iran, its arch-nemesis.
In an historic agreement in late 2016 the OPEC+ group of 24 nations chose to cut 1.8 million barrels of production to revive the oil market from its biggest slump in a generation.
The correction in prices have been a continuing trend since May 23, when prices breached the $80 mark after the announcement of new U.S. sanctions on Iran and ongoing supply disruptions in Libya and Venezuela.
Falih has warned the world could face a supply deficit of up to 1.8 million bpd in the second half of 2018 and that OPEC's responsibility was to address consumers' worries.
Still, the minister told reporters that he was willing to have further discussions about production numbers on Thursday, when he will join a meeting of countries - including Russian Federation and Saudi Arabia - that oversee implementation of the cuts.
"OPEC could keep the same deal with compliance going back to 100%", said an OPEC source who is aware of Iran's stance. "A more relaxed policy will push Brent towards $70 a barrel, while restrictive measures will support crude oil back towards $80".
"This puts Saudi Arabia in a tough position, as unanimity is needed for any accord to be reached", it added.