Human Rights Watch during the weekend said the Iranian and Turkish military response to the Party for Free Life of Kurdistan, or PJAK, and the Kurdistan Workers' Party, PKK, has killed nearly a dozen civilians since July.
Kurdish authorities said villagers fled areas north of Erbil after Iranian forces pounded the area Tuesday.
Iran has thousands of troops deployed along the border with Iraq ostensibly to take on PJAK fighters.
Majid Kavian, deputy commander of PJAK, was killed by shrapnel from Iranian tank bombardments last weekend, the official Islamic Republic News Agency reports.
Tehran notes that the deputy leader joined PJAK in 2003, four years after joining forces with the PKK. The government said Kurdish militants have placed around 5,000 land mines along the Iranian border.
PJAK, in a statement sent to the Voices of Iraq news agency, said it would begin a cease-fire starting Tuesday "or else Iran would be responsible for future incidents."
Human Rights Watch in its report from last week said Iranian military activity along the border regions might be part of an effort to drive civilians out of the area.