"We don't need permission from anyone to cut", said Falih on Thursday.
Saudi Arabia proposed a moderate oil-production cut from Opec and its allies that would gently rebalance the market, seeking to walk a fine line between preventing a surplus and appeasing US President Donald Trump. That, he said, would include production for both OPEC countries as well as non-OPEC countries, like Russian Federation, which have in recent years been coordinating their production limits with the cartel.
Experts say this week's meeting of the Organization of the Petroleum Exporting Countries will influence the price of oil over the coming months. The worldwide benchmark for crude, Brent, was down $1.52 at $60.04 a barrel.
On Wednesday, Trump had taken to Twitter to urge producers to keep pumping.
"Hopefully, OPEC will be keeping oil flows as is, not restricted".
Donald Trump has often complained about OPEC this year as higher crude oil prices have raised fuel cost.
Russia's second-largest oil producer, Lukoil PJSC, is ready to comply with any request from the Kremlin but hopes output cuts won't be necessary, said CEO Vagit Alekperov.
The coordinated move, which has since been extended, stimulated a long rally in oil prices right up until October 2018. Al-Falih said his preference was for a reduction extending into the third quarter.
In the Middle East, Saudi Arabia produced a record 11.3 million barrels per day (bpd) in November, adding to the swelling glut.
OPEC is also riven by internal conflict, especially between regional rivals Saudi Arabia and Iran. The United States is not part of any output-limiting initiative due to its anti-trust legislation and fragmented oil industry.
Zangeneh said the estimated surplus now on the market amounted to 1.3 to 2.4 million barrels per day.
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Bank of America said it expected Brent and WTI prices to average $70 and $59 per barrel respectively in 2019. If the group's most important ally in the broader Opec+ coalition decides to make a sizable cut, the cartel will follow up.
Although Russia, the largest producer in the wider group known as OPEC+, agreed to a cut in principle, the eventual size of their contribution remains undefined and will be key to putting together the final deal.
Since overtaking Saudi Arabia, many in Washington feel the USA no longer needs to shackle itself to Riyadh.
One issue that might complicate relations between the United States and OPEC is the murder of Saudi Arabian journalist Jamal Khashoggi by people linked to the government in Riyadh.
Trump has continued to support the kingdom despite worldwide outrage over the murder but he is at the same time keeping up the pressure for lower prices.
Iran's Zangeneh said it was the first time a USA president was trying to tell OPEC what to do.
"The stakes are high now for OPEC", he said.
Negotiations between OPEC members are fraught, however, as some feel that Saudi Arabia wields too much clout in setting policy.
Qatar, which will leave on January 1, played only a small role in the organisation, providing just under two percent of OPEC's total output.
The deal is monitored by the Joint OPEC/Non-OPEC Ministerial Monitoring Committee (JMMC), which is dominated by Saudi Arabia and Russian Federation. "They are blockading our country", he told journalists.
"I don't think they want to meet me".