The attacks on Wednesday which occurred on a stretch of Zaitoun Street in central Baghdad also hit near a home owned by interim Prime Minister Ayad Allawi, according to police officers.
Allawi was not present at the home at the time, said an Interior Ministry official.
About an hour later, another explosion rocked Baghdad. The US military had no immediate word on the Wednesday morning explosions.
The attacks came only hours before the interim government was set to unveil a law giving Allawi the authority to impose emergency measures to safeguard the country's security.
The new law gives Iraqi officials the ability to institute martial law for limited periods of time and under special circumstances.
The assault marked the second time Allawi's party the Iraqi National Accord was targeted.
Allawi was put under a death sentence last month in an audiotape posted on an Islamist web site in the name of al-Qaida-linked Abu Mussab al-Zarqawi, blamed by the Americans for much of the violence sweeping across Iraq.
"Allawi ... you have escaped many times, without knowing it, from well organised ambushes that we laid," says the voice, purportedly that of Zarqawi.
"But we pledge to go all the way without giving up so that you will meet the same fate as Izzidine Salim," head of the now dissolved Governing Council who was assassinated in a Baghdad car bombing on 17 May.
In turn, an armed group calling itself the "Salvation Movement" threatened in a video aired on Tuesday to kill Zarqawi if he did not leave Iraq.