The vote delivered a resounding "yes" but drew sweeping reprisals from Baghdad which have dealt a heavy blow to the autonomous region's economy.
In its second largest city Sulaimaniyah, security forces fired in the air to disperse demonstrators marching on the central Saray Square, an AFP correspondent reported.
Roadblocks sprang up across the city on major roads and around the offices of the main political parties.
Sulaimaniyah is a bastion of opposition to former regional president Massoud Barzani, who organised the independence vote, but all five of the region's main political parties saw their offices attacked today.
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"You're incapable -- incapable of defending the disputed areas and incapable of ruling the Kurdistan region," one demonstrator shouted.
The disputed areas are a large swathe of historically Kurdish-majority territory outside the autonomous region that Kurdish leaders have long wanted to incorporate in it.
The Kurds took control of many of them during the fightback against the Islamic State group from 2014.
Barzani announced he was stepping down in late October after the independence vote backfired.
Legislative and presidential elections in the region due on November 1 were postponed because of the turmoil.
Prime minister Nechirvan Barzani, the ex-president's nephew, has pledged to hold the polls over the next three months.
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