At least 30 other people were reportedly wounded in the explosion, Colonel Dawood al-Marawi, police spokesman in nearby Falluja, told the Reuters news agency.
Kamal al-Ayash, spokesman for the Fallujah town council, said that the bomber blew himself up as the council leader was meeting senior members of a so-called "Awakening" group.
"At least 11 senior members of the Awakening group have been killed," he told the AFP news agency.
The "Awakening" groups of Sunni tribes have been largely credited with subduing the violence in al-Anbar by forming local armed groups to fight those loyal to al-Qaeda in Iraq.
Police told the AP news agency that the bomber entered the building through a back door, but it was unclear how he managed to evade security.
Colonel Fawzi Fraih, civil defence director of al-Anbar province, told AP that the group was meeting spme Americans when the attack occured.
However, the US military did not immediately confirm whether any Americans were inside the building at the time.
The attack came just days before Iraqi forces were due to take control of security in the province from the US military.
Al-Anbar, the largest province in Iraq, would be the tenth of Iraq's 18 provinces to be handed back to Iraqi forces.
Later on Thursday, three US marines and two interpreters were killed west of Baghdad, officials said.
The military said that they were killed in al-Anbar province but did not say whether they were killed in the suicide bombing on Thursday.
The death toll of US marines in Iraq since the March 2003 invasion now totals 4,113 according to Agence France-Presse news agency.