The mob broke windows and destroyed furniture on Wednesday, said FIT spokesman Turkif Rashad.
"We don't know if these acts were committed in the name of the Patriotic Union of Kurdistan (PUK) or the Kurdistan Democratic Party (KDP)," he said.
But representatives of the two main Kurdish parties said they had no links with the assailants.
The local police chief said an inquiry has been launched and that occupation troops would search the offices of the two parties, as well as those of FIT and others, for weapons.
A curfew has been imposed on the city, 255km north of Baghdad, since 29 February when FIT's offices were hit the first time.
The oil city of Kirkuk is a hotbed of ethnic tensions among the Arab, Kurdish and Turkmen communities and attacks are regularly launched there on the police, US occupation soldiers and oil lines.
Meanwhile, unknown attackers injured two Iraqi policemen when they fired a rocket propelled grenade at their car on Wednesday in the city of Hawija, 200km north of Baghdad, said the local police chief.
The assailants escaped and police have launched an inquiry, said Colonel Awad Abd Allah al-Jubburi.