"At the next meeting, which will be held on the 3rd and 4th (of June), there will be no additional reduction, and as for Iraq, we cannot reduce further," Abdel-Ghani said in an interview, his first to foreign media since taking office last year.
In a following statement, he said Iraq is committed to voluntary oil production cuts that started in May and last until the end of 2023, and noted that Iraq was not asked to make any additional such cuts before a June 4 OPEC+ meeting.
OPEC and its allies led by Russia, known as OPEC+, agreed to cut production in late 2022 to support the market as the economic outlook worsened, hitting prices.
Then in a surprise move in early April, Saudi Arabia and other OPEC+ members announced further oil output cuts of around 1.2 million barrels per day.
The announcement helped push oil prices sharply higher, but those gains have since been erased as fears of a global economic slowdown took hold.
Brent crude futures LCOc1 were at $75.25 a barrel at 1710 GMT, set to end the week flat after three weeks of decline.
OPEC+ members are set to meet in Vienna on June 4 to decide on their next course of action.
"The second cut was voluntary and it has helped us a lot in the stability of the market and boosting prices," Abdel-Ghani said.
The April cuts punished oil short sellers, or those who bet on oil price declines.
Back in 2020, Saudi Energy Minister Prince Abdulaziz bin Salman warned traders against betting heavily in the oil market, promising that those who gamble on the oil price would be "ouching like hell".
Iraq said it would cut 211,000 barrels per day (bpd) starting May as part of the voluntary cuts.
Turkey halted 450,000 bpd of its northern exports through the Iraq-Turkey pipeline on March 25 after an arbitration ruling ordered Ankara to pay Baghdad Damages of $1.5 billion for unauthorised exports by the Kurdistan Regional Government between 2014 and 2018.
It is unclear when flows will resume but Abdel-Ghani said on Friday Baghdad had still not heard back on a request to the Turkish state energy company to restart exports.