Kirkuk lies on the boundary between the northern Kurdish region and the rest of Iraq and is at the heart of a long-running dispute between Baghdad and Arbil, the Kurdish regional capital, over territory and natural resources.
Kurdish forces took control of production facilities at the Kirkuk and Bai Hassan northern fields on July 11, exploiting a power vacuum created by an Iraqi military withdrawal in the face of an extremist insurgent offensive.
The Iraqi official told Reuters by telephone from Baghdad, the Kurdish region had started to pump crude from one of the Kirkuk domes to the Khurmala dome, out of which the Kurdish pipeline runs, using an existing connection.
"They are using a pipeline which was originally used to send crude from (Kurdistan), but they have now reversed it (to use it by the Kurdish region)," the official said, estimating the quantity at around 20,000-25,000 barrels of oil per day.
Kirkuk's Baba and Avana geological formations were previously administered by Baghdad before the July 11 conflict.
The Kirkuk region's third formation, Khurmala, has long been under the control of the Kurdistan Regional Government (KRG).
Kurdish forces took control of Kirkuk a month ago after Iraqi troops left in the face of a lightning assault by the so-called Islamic State of Iraq and Levant (ISIL) radicals, who have seized large parts of northern and western Iraq, but not threatened Iraqi Kurdistan.
The Kirkuk and Bai Hassan oilfields have a combined production capacity of 450,000 bpd but have not been producing significant volumes since March, when Iraq's Kirkuk-Ceyhan export pipeline was sabotaged by radical militants.
Last year, Baghdad signed a deal for BP BP.L to revive the Kirkuk oilfield, a plan that the KRG has rejected as illegal.
SHI/SHI