"By any measure, these are prolific wells tapping into what increasingly feels like a sea of oil," Bijan Mossavar-Rahmani, DNO International's executive chairman, said in a statement.
DNO, which has headquarters in Norway, has a majority stake in the Tawke field alongside Turkish energy company Genel Energy and the Kurdistan regional government.
DNO's production from Iraqi developments during the second quarter of 2013 climbed approximately 30 percent.
The company said drilling operations are under way for two additional wells in the Tawke field. Both should be finished by the end of the year.
Oil production from Iraq declined from 3.2 million barrels per day in August to 2.8 million bpd in September, the Organization of Petroleum Exporting Countries said. OPEC's figures included production from the Kurdish north.
The central government considers independent work in the semiautonomous Kurdish north of the country illegal.