Rice was speaking after talks in Washington June 18 with Iraqi Foreign Minister Hoshyar Zebari.
Turkey's government has accused separatist Turkish Kurdistan Workers Party guerrillas of sheltering in the Kurdish northern part of Iraq.
Turkey has refused to rule out taking unilateral action if such activity is not halted.
KURDISH AWAKENING: The ethnic Kurdish region in the northern part of Iraq has struggled in recent years to reestablish its cultural and political identity after decades of oppression under the regime of deposed Iraqi President Saddam Hussein. In December, RFE/RL correspondent Charles Recknagel traveled to this area and filed several reports: