The increase in production follows the country's departure from the OPEC oil cartel, which is dominated by Saudi Arabia, in late April and early May this year.
The previous production record in the country, set in 2020, was 4.0 million barrels per day.
Other countries around the Persian Gulf also increased production in June, according to the IEA, but they did not reach the levels that prevailed before the US and Israel began the bombing campaign against Iran on February 28.
Saudi Arabia's production rose to 7.3 million barrels per day, an increase of 900,000 barrels per day compared with May.
Exports of refined oil products have not kept pace with the upward trend.
