Iran has thousands of troops deployed along the border with Iraq ostensibly to take on fighters with the Free Life Party of Kurdistan, or PJAK. Turkey is busy fighting the separatist Kurdistan Workers' Party, or PKK, along its border.
Both sides have crossed into Iraq during attacks and, in some instances, killed Kurdish civilians during the raids.
Massoud Barzani, president of the Kurdistan Regional Government, in a message to the Kurdish people, said the presence of rebel forces gave his neighbors "an excuse" to launch attacks inside Iraq.
He said the continued use of violence in the Kurdish provinces will lead to further unrest in the area and won't allay regional aspirations.
"It is unfortunate that no consideration is given to the interests and welfare of the people of the Kurdistan region," he added.
Washington said that while Ankara has the right to defend itself, it should keep Iraqi sovereignty in mind. The U.S. military in Iraq has shared intelligence about PKK activity in the country.
"The sooner this fighting ends the better," the Kurdish president said.