Regional rival Saudi Arabia and non-OPEC member Russia want to increase production by about 1 million barrels a day.
Iran has bulked at the request because it faces sanctions after President Donald Trump ripped up an international nuclear agreement. Mr Trump has also increased pressure on OPEC to raise production ahead of mid-term elections.
“I do not think we can reach an agreement,” Bijan Namdar Zanganeh, Iran’s oil minister, said as he stormed out of the meeting on Thursday evening.
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.
There is concern among consuming nations and some OPEC members that a shortage and rising oil prices could cripple the global economy.
OPEC and Russia agreed last year to cut production by 1.8 million barrels a day to lift oil prices that had fallen to a low of $27 in 2016.
But production problems in Venezuela and Libya have seen about 2.8 million barrels removed from daily global supply.
Saudi Energy Minister Khalid al-Falih has signalled a compromise was in the works as a big hike in production was “politically unacceptable” to some members.
“We want to prevent the shortage and the squeeze that we saw in 2007-2008,” Falih said. At that time, oil prices rose to almost $150 a barrel.
“An initial increase of between half a million and a million barrels is expected to be agreed which will be welcomed by Trump who has been targeting OPEC as of late,” Craig Elam, senior markets analyst at OANDA, said.
Brent oil prices rose 1% to 74.03 in London trading on Friday.