Gulf Keystone said its first production facility at the Shaikan field should reach 20,000 barrels per day. The second facility should add another 20,000 bpd, it said.
The company in June said the region's Shaikan field could hold as much as 10.5 billion barrels of oil. The semiautonomous Kurdistan Regional Government said production could reach 250,000 bpd by 2018.
Gross production from the first phase of Shaikan totaled 183,000 barrels of oil and nearly all of it was sold on the Iraqi market.
The Kurdish provinces of Iraq have been relatively shielded from violence. A bomb struck the Kurdish capital, Erbil, in late September. Gulf Keystone, which has headquarters in London, said its facilities weren't affected by the bombing.
The KRG has been locked in a heated debate over oil revenue with the central government in Baghdad.