Hospital officials said six people were killed, including the man who had been freed. Another 10 people were wounded in the blast.
On Saturday, two suicide bombers killed six policemen and wounded 13 others outside a police station west of Ramadi in Anbar.
Al-Issawi was a member of the town's awakening council, which is credited by the US for improving the security situation in the province.
The US military meanwhile reiterated its accusation that Iran was a "negative influence" in Iraq.
Rear Admiral Gregory Smith, a US military spokesman, told reporters in Baghdad on Sunday that although there had been a dramatic drop in the number of Iranian weapons being smuggled into Iraq, the Islamic Republic continued to exert a "negative influence" in Iraq.
Smith also said al-Qaeda is increasingly being forced to use suicide attacks because its ability to stage large-scale bombings has been diminished.