Guards shot dead two demonstrators in Kalar on Saturday as protesters tried to storm the local headquarters of the Kurdistan Democratic Party (KDP), a hospital official said.
"Two protesters have died of bullet wounds. One was 19 and the other 40," the official told AFP, adding that 19 people were wounded.
Witnesses and a security official said the protesters eventually set fire to the local KDP office in Kalar, a town in the southernmost part of Iraq's Kurdish region.
Two protesters were shot dead in similar circumstances yesterday in Qala Diza, further north.
The demonstrations were initially protests against the non-payment of salaries to civil servants by the Kurdish Regional Government, which faces a dire budget crisis.
They have evolved into a mobilisation against Barzani in areas of Iraqi Kurdistan where opposition to the KDP is traditionally strong.
"Our demands are not only focused on corruption and salaries but they now include Barzani's removal," said Nazar Mohammed, a civil society activist and one of the organisers of the protest in Sulaimaniyah.
Mohammed argued that the political class's inability to solve the crisis showed disregard for regular citizens.
"The main parties don't care about the people. All they worry about is the presidency, all this at the detriment of the people who are in a bad economic situation," he said.
Some protesters tried to storm the Sulaimaniyah office of the Kurdish TV station Rudaw, which is owned by the Barzani family.
Minar Mohammed, the head of the local hospital, said 25 people were lightly injured in scuffles during the Sulaimaniyah protest.
No such protests have yet taken place in northern and western regions traditionally more loyal to the KDP.
