Dozens of people broke away from the march and ran at the gates of the parliament's main building, Leinster House.
They wrestled with police, who tried to force them back and secure the gate.
At least one man suffered a head injury during the scuffles with organisers appealing for calm.
Officers stopped the protesters from breaching the gate.
Gardai said no arrests were made and the scuffle was brought under control within minutes.
One man was seen walking away with blood dripping from the back of his head.
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