The surplus seen between May and July ought to be compensated for in August and September, the report said.
OPEC+ – which includes members of the Organization of the Petroleum Exporting Countries and other producers including Russia – stepped up their joint output cuts to a record 9.7 million bpd in May before tapering them to 7.7 million bpd this month.
In April the impact of the new coronavirus on air and road travel and other areas of the global economy sent benchmark oil prices below $16 a barrel.
The ongoing spread of the virus is now threatening oil demand recovery forecasts.
The internal report seen by Reuters did not say how the additional cuts would be distributed over August and September. But if the 2.31 million bpd figure is adopted and spread equally over the two months, it would take OPEC+ oil cuts to about 8.85 million bpd.
The report shows OPEC+ expects oil demand in 2020 to fall by 9.1 million bpd, 100,000 bpd more than in its previous forecast, before rising by 7 million bpd in 2021.
However, OPEC+ also see an alternative scenario in which a stronger and more-prolonged second wave of infections hits Europe, the United States, India and China in the second half of the year.
Under this scenario, demand is forecast to fall by 11.2 million bpd in 2020, sending OECD commercial oil inventories in the fourth quarter to 233 million barrels above the latest 5-year average, the report showed.
Stocks would stand at 250 million barrels above the latest 5-year average in 2021.
Data shows among OPEC members, Iraq and Nigeria were the least compliant and even the United Arab Emirates, which made additional voluntary cuts in June, overproduced by around 50,000 bpd over the May-July period.
Among non-OPEC participants, Russia and Kazakhstan overproduced by 280,000 bpd and 190,000 bpd, respectively.