The suicide car bombs struck a police checkpoint near Ramadi, the capital of mostly Sunni Anbar province, killing at least five policemen and wounding eight others, officials said.
And north of Baghdad, a parked vehicle rigged with explosives detonated in the restive town of Muqdadiyah, killing 10 Iranian pilgrims and wounded 30 others.
The blast occurred as the pilgrims' bus passed through the town en route from the Iranian border to the Shiite holy city of Najaf.
Shiite Muslims visiting shrines and religious sites form the backbone of Iraq's tourism industry, with the vast majority of pilgrims coming from Iran.
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When completing a tour of Iraq's key Shiite religious sites, pilgrims typically visit Najaf, nearby Karbala, Baghdad, and Samarra, the latter of which lies north of the capital.
Sunni militants, including those linked to Al-Qaeda, view Shiites as apostates and often target them. However, no group immediately claimed responsibility for today's bombing.
Attacks in Iraq have risen sharply, with May the deadliest month since 2008, as persistent political disputes have given fuel and room for militants to increase their activities.
The UN envoy to Iraq has warned that the violence is "ready to explode".