Earlier, an Iraqi soldier was killed and 10 others injured in a roadside bomb blast directed at an army patrol in the Abu Nawas area of the city, an interior ministry official said.
The blasts came a day after police reported a day of calm in Baghdad, saying there had not been a single bombing in the capital on Wednesday.
Iraqi police and troops have taken control of security in urban areas after US troops pulled out of towns and cities in the country at midnight on Tuesday.
'Despicable defeat'
US and Iraqi officials had said they expected insurgents to try to take advantage of the pullback to launch more attacks and to test the Iraqi defence forces.
The leader of the Islamic Army in Iraq, thought to be the military wing of Saddam Hussein's outlawed Baath party, claimed the US withdrawal was a victory for insurgents, according to the Site Intelligence Group.
"If anyone has a right to celebrate victory, it should be the resistance and its men and those who rallied around it and supported it among the children of our people and our Ummah (nation)," the "emir" of the group said in an online message monitored by Site.
"They are the ones who brought the occupation to a despicable defeat and made their remaining forces in Iraq demanding and very costly," he said.