"We have started testing operations at Avana and Bai Hassan oilfields to prepare initial pumping of more than 50,000 barrels per day," one NOC official said.
Operations at the Avana and Bai Hassan fields have been halted since October, when Iraqi forces took them back after they had been under Kurdish control since 2014.
Oil exports from Kirkuk fields have been suspended amid an ongoing dispute between Baghdad and the Kurdish Regional Government (KRG) over the use of the Ceyhan export pipeline to Turkey.
Iraqi oil officials said there were no plans to resume crude flow through the Kurdish-owned pipeline, as no agreement had been reached yet.
"Until this moment we didn't reach any kind of agreement, even an initial, with Kurdish authorities to resume Kirkuk oil exports to Ceyhan," said an oil ministry official.
The Kurdish region operates a pipeline that connects to the twin Kirkuk-Ceyhan pipeline at Khabur on the border with Turkey.
Iraq started late last year to divert output from Kirkuk oilfields to local refineries to boost fuel production and help free up more oil for exports from the southern oilfields.