The gunmen overnight sprayed bullets in the air and torched the office in the Shi'ite city of Karbala, 80 kilometers south of Baghdad.
On 4 December, a hostile crowd in the nearby city of Al-Najaf threw stones, shoes, and tomatoes at Allawi, a secular Shi'a.
The United Nations has expressed "serious concern" over violence ahead of the parliamentary elections scheduled for 15 December.
(AFP/dpa)