The moves escalated a feud between the Shi'ite-led central government and the autonomous Kurdish region driven by a Sunni insurgency that threatens to fragment Iraq on sectarian and ethnic lines.
Kurdish forces yesterday took over production facilities at the Bai Hassan and Kirkuk oilfields near Kirkuk, the oil ministry in Baghdad.
The oil ministry called on the Kurds to withdraw immediately to avoid "dire consequences".
Kurdish forces took control of Kirkuk a month ago after Iraqi armed forces withdrew in the face of an assault by Islamic State militants, who have seized large parts of north and west Iraq.
The two oilfields have not been producing significant volumes of oil since March, when an export pipeline was sabotaged.
Efforts to reach agreement on a new Iraqi government to confront the insurgents have been complicated by the rising tensions between Maliki and the Kurds.
The national parliament elected in April met for the first time last week. The United States, the United Nations and Iraq's own Shi'ite clerics have urged lawmakers to form a new government to face the Sunni insurgency quickly.