At least nine bombs exploded in the latest violence targeting markets, security checkpoints and a minibus.
Thousands of extra Iraqi troops had been deployed on the streets, manning checkpoints in a highly-visible security operation.
Iraqi officials were hoping to exploit any power vacuum in insurgent ranks following the death of Al-Zarqawi in a US air raid on a house north of the capital ten days ago.
A new statement posted on the internet, purporting to be from Al-Qaeda, vowed to avenge the commander's death.
In his weekly radio address, US President George W. Bush acknowledged that serious challenges remained in Iraq but promised the Iraqi people that America would not abandon them.