The suicide bomber outside Allawi's Iraqi National Accord party headquarters posed as a taxi driver, killing two policemen and a civilian and wounding 25 others. Aides said Allawi was not near the scene at the time.
The bomber tried to ram through a checkpoint leading to Allawi's offices, but his car hit a police pick-up truck and blew up, according to Reuters.
The Iraqi militant group Army of Ansar al-Sunna claimed responsibility for the bombing on its Web site. The group also has taken credit for a Dec. 21 attack on the U.S. military mess hall near the northern city of Mosul in which at least 22 people died.
Another attack on Monday occurred in Balad, about 50 miles north of Baghdad, killing four Iraqi National Guardsmen and injuring 14 others, said U.S. military spokesman Neal O'Brien. The driver of the car bomb also died in the blast.
A third strike Monday took place in Saddam Hussein's hometown of Tikrit when a roadside explosion killed at least six Guardsmen and wounded four others, the Associated Press reported.
The latest string of attacks came a day after a suicide bomber detonated his car next to a bus carrying Iraqi National Guard troops in Balad, killing at least 22 Guardsmen and their bus driver. Ten others were killed in separate attacks over the weekend.
In Mosul, a beheaded, booby-trapped corpse exploded as police were trying to identify the body, killing an Iraqi policeman and injuring two others, according to a government statement.
"This is another example of how the criminals and terrorists -- attempting to thwart Iraq's efforts to conduct free and fair elections -- have no regard for their fellow countrymen," the government said.
Meanwhile, Iraqi Defense Minister Hazem Shaalan raised the possibility that elections set for Jan. 30 could be postponed to try to persuade the minority Sunni Muslims to participate, according to the AP.
Shaalan said during a trip to Cairo, Egypt, that he asked Egypt to try to persuade Sunni Muslims to participate.
"We could postpone the date to let all Iraqis go to the polls in one day," he said.
Other Iraqi and U.S. officials, including President Bush, have insisted the vote must take place on its planned date.
Shiites, who make up the majority of the country's population, are anxious for the vote to proceed so they may take power long denied them under Saddam Hussein's Sunni regime.
Al-Qaida leader Osama bin Laden has urged Muslims not to vote, calling the election illegitimate in a tape released Dec. 27.