Shootings and blasts in the capital came a day after a twin bombing by a jihadist group on a Shiite political rally there killed 36 people, the deadliest single attack during campaigning for Wednesday's polls.

Prime Minister Nuri al-Maliki is seeking a third term on Wednesday, with voters citing a long list of grievances ranging from poor electricity and sewerage services to rampant corruption and high unemployment.

A bomb inside a central Baghdad cafe killed three people on Saturday, and gunmen killed four others in shootings around the capital, security and medical officials said.

In Salaheddin province north of Baghdad, a series of attacks left eight people dead.

In one incident, gunmen killed four soldiers, while militants elsewhere in the province killed a provincial councillor and three of his guards.

Also in Salaheddin, insurgents detonated bombs at two polling centres but did not cause any casualties.

A police officer said at least two of the Baghdad assassinations appeared to be revenge attacks for Friday's twin bombings targeting the political rally.

Friday evening's car bomb followed by a suicide attack hit a rally for the Sadiqun bloc, the political wing of the Asaib Ahel al-Haq (League of the Righteous) militia, killing 36 people.

The League of the Righteous, a Shiite militia previously blamed for killing US soldiers and kidnapping Britons, has been linked to groups fighting mostly Sunni rebels in Syria, whose civil war has split the Middle East's sectarian communities, particularly in multi-confessional Iraq.

The Islamic State of Iraq and the Levant (ISIL) claimed the attack, saying it wanted to avenge the League's involvement in neighbouring Syria.

ISIL, itself fighting in Syria, made the claim in a statement on jihadist forums hours after the attack.

It was "in revenge for what the Safavid militias are doing in Iraq and Sham (the Levant), killing and torturing and displacing Sunnis," it said.

It used a pejorative term for Iraq's Shiite majority, linking it to the Safavid empire that once ruled predominantly Shiite Iran.

- 'Criminals targeted us' -

Earlier on Saturday, the League of the Righteous held funerals for several of the victims in the holy city of Najaf, south of Baghdad, where Shiites are typically buried, an AFP journalist said.

"Defending holy sites in Syria, and our support for the (Iraqi) state and security forces in their war against terrorism pushed these criminals to target us," one mourner said.

Iraqis will vote with no sign of a let-up in the violence, and the country still needing to rebuild after decades of conflict and sanctions.

Several Shiite blocs are competing with Maliki for votes in his traditional heartland of central and southern Iraq.

They include Sadiqun but also the Ahrar movement, which is linked to powerful cleric Moqtada al-Sadr, and the Citizens bloc, a formerly powerful political group seen as close to Iran.

The League of the Righteous joined the political process in early 2012, shortly after American forces left Iraq.

Washington has accused Iran of funding and training the group, a charge Tehran denies.

The group broke away from Sadr's Mahdi Army in 2004, and has also been blamed for the kidnap of British IT consultant Peter Moore and his four bodyguards in 2007.

Moore was released, the only member of the group to survive.

The group is also suspected of being behind an attack in January 2007 in which a US soldier was killed and four others were abducted and later found dead.