The fighting took place in a number of Kurdish-dominated towns, leaving at least six Iranian soldiers dead. The number of causalities on the Kurdish side has not been confirmed yet.
One of the dead among Iranian forces was Samad Boostani, a deputy commander of Iran's elite Revolutionary Guards in the city of Shno, a Kurdish official told VOA.
Kurds in Iran have long desired more autonomy from Tehran's firm grip, and they have found assistance in the Kurdish forces in Iraq.
Kurdish fighters, affiliated with the Kurdistan Democratic Party of Iran (KDPI), say their goal from this campaign is to force Iran to make political concessions.
"We are not proponents of military option, but the Iranian regime is forcing us to go in that way," Rostam Jahangiri, the military head of KDPI, told VOA from his base in the Kurdistan Region of Iraq.
The majority of Iranian Kurdish fighters have been stationed in northern Iraq for years, but recently some of them have managed to cross the border into Iran.
Ethnic Kurds make up roughly 9 percent of Iran's total population, living primarily in the western and northwestern provinces of the country.
Iranian officials say that they're fighting "terrorists" who intend to destabilize the country.
The Iranian army "let them infiltrate a mile into Iranian territories to trap them and then killed scores of them," said a journalist of Sepah News, a state-run Iranian news agency. He spoke to VOA on condition of anonymity.
The reporter said that seven Iranian soldiers were killed in the clashes and 11 Kurdish rebels were reported dead. Kurdish officials have not confirmed their causalities.
Iran has been heavily involved in Syria's civil war since 2011, backing forces of Syrian President Bashar al-Assad with Revolutionary Guards troops.
Emboldened by Kurdish advances in Syria and Iraq, Iranian Kurdish groups say it is time for them to push Tehran to acknowledge their ethnic rights.
"Our goal is start to a popular movement that is a combination of political activism and military campaign," said Jahangiri of the KDPI.