Group claims responsibility
On Saturday, a statement posted on an Islamist website in the name of the Islamic Emirate of Iraq group said it carried out the attack.
"The chances of success [in Iraq] are essentially zero because the Iraqi people have no voice"
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The group said its fighters had "succeeded with Allah's help" in striking Zubayi.
"We pray to God not to save the life of this inferior traitor who sold his religion and his people for a cheap return," added the statement.
The statement said the group would reveal more details about the bombings later.
Dhafter al-Ani, a member of parliament for the National Concord Front, the main Sunni bloc to which Zubayi also belongs, said the suicide bomber came from the deputy prime minister's own security unit.
"The suicide bomber was one of his bodyguards and he was recruited by the Islamic State of Iraq." he told AFP.
The suicide bomb attack was followed minutes later by a car bombing close by.
The double attack killed nine people and wounded 15 others.
At least eight people were killed and more than a dozen wounded in attacks in Baghdad on Saturday, including a suicide truck bombing against a police station, security officials said.
Five people were killed and 10 wounded, mostly policemen, when the bomber blew up his truck near a police station in the Sunni southern Baghdad district of Dura.
Four policemen were among the dead and eight among the wounded, a defence ministry official said.
In south Baghdad's Abu Chir district, mortar fire killed three people and wounded seven more, including two women and a child, the official said.