The summit is seen as the country's debut on the regional stage following the withdrawal of US troops in December and Iraq's government is anxious to show it can reinforce security to host its neighbours.
The deadliest attack on Tuesday occurred in the southern holy Shia city of Kerbala, where twin explosions killed at least 13 people and wounded 48, the sources said.
In the northern city of Kirkuk, a car bomb exploded near a police headquarters, killing seven and wounding 30.
In central Baghdad, a suicide car bomber killed three people and wounded 21.
Blasts also occurred in Baiji, Samarra, Tuz Khurmato, Daquq and Dhuluiya, all north of Baghdad, and Hilla and Latifiya in the south.
Although violence in Iraq has declined since the height of sectarian fighting in 2006 and 2007, bombings and shootings still occur on a daily basis nine years after the 2003 US-led invasion.
On Monday evening, bombers struck five times in the northern Diyala province, killing at least three people and wounding more than 30, police said.
The Arab League summit is due to be held in Baghdad on March 27-29.
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