Car bombs and attacks on cities across Iraq killed at least 20 people and wounded more than 200, officials said.
The wave of attacks in Baghdad, Kirkuk, Nassiriya, Tuz Khurmato and other towns, came days before Iraqis vote in provincial elections.
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The Prime Minister has praised the former soldier's "huge professionalism" in trying to save the life of Pc Keith Palmer.
The man who carried out the Westminster attack is thought to be British born and was once investigated by MI5, the Prime Minister has said.
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