Mr Zanganeh has said the president is to blame for high prices because of his unilateral withdrawal from the worldwide nuclear agreement and the imposition of fresh sanctions that could significantly curb Iran's crude exports.
Support for the increase, which had been proposed by Saudi Arabia against objections from Iran, was unanimous, he said.
"I don't think we can reach agreement" on the proposal, Zanganeh said as he left the meeting.
Oil prices rose in early Asian trading on Wednesday, supported by a drop in US commercial crude inventories reported by the American Petroleum Institute (API).
US President Donald Trump was among those wondering how much more oil OPEC will deliver.
The tentative increase is less than many market participants feared, and helped buoy oil prices back above $75 a barrel from less than $73 a barrel earlier this week. Worldwide benchmark Brent crude has since rebounded to about $75 a barrel.
"Saudi Arabia and Russian Federation continued to push for a relaxation in production constraints, going against many other members wishes", ANZ bank said on Wednesday. "Hope OPEC will increase output substantially".
That would effectively mean a boost from producers such as Saudi Arabia that have voluntarily cut more deeply than planned.
Resistance is being led by Iran, deeply wary of any move by regional rival Saudi Arabia that could push down oil prices at a time when Tehran faces renewed sanctions following US President Donald Trump's decision to quit its global nuclear deal, which is likely to impact the country's oil exports.
Ecuador said OPEC and its allies could agree to a compromise increase in output of around 0.5-0.6 million bpd.
"There is a lot more at stake than just ticking a box and say: 'we got this out of the way", the minister said, nothing that "timing isn't critical for the government of Saudi Arabia".
If all Opec members produced as much as they were allowed under the deal, Opec output would in theory rise by about 740,000 barrels per day, based on Reuters estimates of the group's production in May.
Iran, with some support from Venezuela, has so far rejected any increase, including one compromise mooted in private by some OPEC officials for a 300,000-to-600,000 barrel-a-day hike in the second half of the year.
Iran is usually not part of the committee, which groups Russia, Saudi Arabia, the United Arab Emirates, Oman, Kuwait, Algeria and Venezuela.
He said that the world could face a supply deficit of up to 1.8 million barrels a day in the second half of the year, and maintained that it is OPEC's responsibility to address that imbalance. In September, we will review the situation in the market and decide the future course, ' he said.
Al-Falih also said leaders from other countries including India, China and South Korea had also expressed concerns to him that their economies were "starting to feel the pinch of higher oil prices".