The bomber reportedly drove into a crowd and blew himself up as mourners walked down a main street carrying the coffin.
Al-Fallujah is the capital of the restive Al-Anbar Governorate, a stronghold of the Sunni Arab-led insurgency and of Al-Qaeda militants.
Separately, the U.S. military said two of its soldiers were killed in Al-Anbar on May 23.
Earlier, the military had confirmed that a body pulled from the Euphrates River near Baghdad on May 23 was that of one of three missing U.S. soldiers.
The soldier went missing with two comrades after their patrol was ambushed on May 12 in Al-Mahmudiyah, an insurgent stronghold south of Baghdad.
In political developments, Iraqi Prime Minister Nuri al-Maliki today nominated ministers for six cabinet seats that loyalists of radical Shi'ite cleric Moqtada al-Sadr vacated in April.
In a speech before announcing the six names, al-Maliki insisted that the nominees were independent technocrats.
Al-Sadr's ministers withdrew from the government in response to al-Maliki's refusal to back a timeline for the departure of international forces from the country.
(AFP, AP, Reuters)
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