Fighters from the mainly Shi’ite Hashid Shaabi militia, together with Iraqi security forces, are preparing a counter-attack in Anbar against Islamic State after the militants seized the provincial capital Ramadi in mid-May.
Police say at least 14 people have been killed and more than 40 wounded in a series of bombings across the Iraqi capital.
The northeastern area of Al-Shaab was rocked by two explosions, at least one of which was caused by an attacker who detonated his suicide vest, a police colonel and an interior ministry official said.
There had been fears that IS would intensify attacks in Baghdad during Ramadan, but with the fasting month nearing its end, no surge in bombings has taken place.
Another bomb in the Iskan district of western Baghdad killed two people, medical sources said.
In Rashidiya just north of Baghdad, they say a bomb exploded near a vegetable and fruit market, killing three people and wounding five.
A local hospital official corroborated the casualty figure.
All spoke on condition of anonymity as they are not authorised to brief journalists.