Legislators were seen climbing desks and tearing up papers in a video posted to the legislature's YouTube channel, while footage shared by Iraqi media showed lawmakers trading punches.
"It was anarchy and they attacked members from our bloc," said Ziad Jabbar, house leader of the Patriotic Union of Kurdistan (PUK), during a press conference.
Asked by a journalist why he had bloodstains on his shirt, he said he had suffered a blow to the head in the fracas.
Elections had been scheduled for late 2022, but disputes between the leading Kurdistan Democratic Party (KDP) and the PUK forced the assembly to extend its mandate for another year.
Fresh elections for the 111-seat parliament are planned for November 18. The KDP currently holds 45 seats, trailed by the PUK which has 21.
The tumult broke out after the KDP scheduled a late vote to activate the commission organising the elections.
PUK lawmakers wanted the vote postponed, with each side accusing the other of procedural irregularities.
Jabbar charged that the KDP had "refused an adjournment of the parliamentary session... thus causing tension and chaos".