Fighters from a group known as Ansar al-Islam (supporters of Islam) took two PUK hilltop positions near the city of Halabja, close to the Iranian border, according to the Associated Press news agency.
The agency quotes a PUK commander as saying 20 of his fighters were killed or injured in the fighting.
Battles between the PUK and Ansar al-Islam have intensified over the past year in eastern parts of Kurdish-controlled northern Iraq.
The Ansar are largely made up of Iraqi Kurds belonging to several Islamic groups which merged late last year.
They are also believed to include Arab fighters formerly based in Afghanistan, and thought to have links with the al-Qaeda network.
No rest
The Ansar fired heavy artillery as they charged the Kurdish positions, PUK commander Sheikh Jaffar Mustafa told AP.
He said the Ansar had succeeded because the PUK had sent some of its forces on leave for the Muslim holiday of Eid el-Fitr - which marks the end of the holy month of Ramadan.
"They took advantage of the situation," Mr Mustafa said.
"Everywhere in the Muslim world people usually stop fighting for Ramadan," he added.
The PUK controls the eastern part of the autonomous zone in northern Iraq. Western areas are controlled by its rival, the Kurdistan Democratic Party.
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