Sunni complaints prompted the country's Sunni vice president to threaten to leave the Shi'ite-dominated government unless key unspecified amendments to the constitution are not made by May 15.
The power struggle among the Sunnis, which surfaced last year, could prove decisive in the US campaign to win over significant portions of the Sunni community, which has formed the bedrock of the insurgency.
The first of the Ramadi area attacks happened about noon in a market on the northwest outskirts of the city, killing eight people and wounding 13, said police Colonel Tariq Youssef.
About 15 minutes later, police at a nearby checkpoint spotted a second car bomb and opened fire, but the driver was able to detonate the vehicle, Youssef said. Five people, including two police officers, were killed and 12 were wounded, Youssef said.
The attacks occurred in areas controlled by the Anbar Salvation Council, an alliance of Sunni tribes formed last year to drive Al Qaeda from the area. Council officials blamed the attacks on Al Qaeda.
"They committed this crime because we have identified their hideouts and we are chasing them," said Sheik Jabbar Naif al-Dulaimi.
In a Web statement yesterday, an Al Qaeda front organization, the Islamic State of Iraq, warned Sunnis against joining the government security forces -- a move supported by the Salvation Council.
"We tell every father, mother, wife, or brother who does not want to lose a relative to advise them not to approach the apostates, and we swear to God that we will use every possible means to strike at the infidels and the renegades," the group's statement said.
The Islamic State also claimed responsibility yesterday for attacks that killed 34 people over the weekend -- including six US soldiers and a Russian embedded photojournalist who died in a roadside bombing in Baqubah.