A second attack struck in the nearby town of al-Jazeera 15 minutes after the first explosion when a car approached a police checkpoint.
It is reported that five officers and seven members of the public were killed in the blast while a further 25 people were injured in the incident.
Tareq al-Thiyabi, an Iraqi government security adviser, linked the attack to an ongoing fight between local tribal chiefs and al-Qaida. "They are terrorists," he said. "They are from al-Qaida."
Ramadi is in the volatile Anbar province which has a predominantly Sunni Arab population.
The US military believes it is achieving some success in reducing the violence in the area by working with the local tribal leaders.
However these attacks come in the wake of yesterday's suicide bomb in Baghdad where 25 people were killed.
The US is currently reinforcing the number of troops it has in the area around Baghdad, including Ramadi, and expects to have a further 30,000 soldiers in place by June 1st.
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