The attacks by explosives-laden drones and rockets targeted the opposition Kurdistan Freedom Party (PAK), the Kurdistan Democratic Party of Iran (KDPI), the Free Life Party of Kurdistan (PJAK) and Komala in the provinces of Erbil and Sulaymaniyah, Kurdish media reported.
At least 32 others were also injured as a result of the strikes, Iraq's state news agency INA quoted Barzinji as saying.
Initially, Barzinji said at least three people had died and 16 others were injured.
The Iraqi Foreign Ministry said it would summon the Iranian ambassador in Baghdad to hand him a "strongly worded" protest note.
The Kurdistan regional government condemned the attacks.
"Attacks on opposition groups through the Islamic Republic of Iran's missiles, under any pretext, is an incorrect stance which promotes a misleading interpretation of the course of events," it said in an English statement.
"We strongly condemn these continuous attacks which result in the death of civilians and we call for an end to these violations."
Earlier on Wednesday, Kurdish media circulated videos of rockets in the sky and plumes of smoke following the attacks.
A video posted on the news website Kurdistan 24 showed schoolchildren panicking, allegedly due to Iranian strikes on KDPI positions in the town of Koya in the province of Erbil.
The attacks were the third in the past five days to target Kurdish separatist groups' bases in northern Iraq, according to the Iranian Tasnim news agency.
The Iranian Revolutionary Guards called the attacks a "legitimate reaction" to Kurdish groups' attacks on Iranian military bases in the border area in the past, Tasnim said.
Iran's Interior Minister Ahmad Wahidi had previously accused some Kurdish groups of being involved in the anti-government protests in Iran that were triggered by the death of 22-year-old Iranian woman Mahsa Amini while in custody for violating the country's strict Islamic dress code.
Iran has also accused the Kurds of supplying arms to the protesters.
Amini had Kurdish roots and lived in Kurdistan with her family for some time.