Genel said in a Thursday update on its operations in the Kurdish region of Iraq combined gross production from the Taq Taq and Tawke fields was 229,000 barrels of oil per day for June.
The company in March blamed a 2013 fire at the Taq Taq field and "pricing sensitivity in the domestic market" for earlier production shortfalls.
"Genel's operations in the Kurdistan Region of Iraq remain safe and secure," it said in its Thursday update.
Sunni insurgents declared an Islamic state in the region after taking control over key cities in northern Iraq last month. The semiautonomous Kurdish region has been shielded from most of the violence.
Genel said combined output from the two Kurdish oil fields has averaged 88,000 bpd for the first half of the year.
Kurdish oil was exported from the Turkish sea port of Ceyhan last month. The federal government in Iraq said the sales were illegal because they didn't have the consent from Baghdad.
"Proceeds from the first cargo, sold at international prices, have been paid into a bank account in Turkey controlled by the Kurdistan Regional Government," Genel's update said.