A rally in Sulaimaniyah, along with another protest in the same city, was the latest in a string of nationwide protests that have drawn thousands out to denounce high level corruption, unemployment and poor basic services.
"The authorities in the region do not understand what democracy means," said Frishta Karim, a 21-year-old student. "We firmly reject the use of weapons against demonstrators."
Police at the rally refused to allow the protesters to exit the university campus, according to an AFP journalist at the scene.
One banner in Saturday's demonstration called on Barzani, whose Kurdistan Democratic Party (KDP) is the dominant political force in the region, "to apologise to the people of Sulaimaniyah for his guards' shootings."
On Thursday, two young men were killed and 54 others were wounded when KDP guards fired into the air in an attempt to stop protesters from reaching KDP's headquarters in Sulaimaniyah, the autonomous Kurdish region's second city.
Around 1,000 people were at Sulaimaniyah's main square on Saturday demanding the release of individuals arrested in connection with Thursday's rally, and the prosecution of the head of the city's KDP office who, the protesters said, gave the order for security to open fire.
Barzani has called for a full investigation into the incident.
Immediately after Thursday's protests, looters attacked the offices of opposition movement Goran in Arbil and Dohuk provinces, which along with Sulaimaniyah make up the Kurdish region.
Goran denied it was part of the Thursday demonstration.