A female suicide bomber blew herself up near an entrance to the US-protected Green Zone today, Iraqi officials said.
In a separate attack, a bomb tore through a minibus carrying Iraqi government employees.
Meanwhile, three people were killed in bomb attacks on police patrols in Baghdad and Baqouba, northeast of the capital, police said.
The violence, during the morning rush hour, in which at least 20 people died, came as Iraqi MPs prepared for a vote on Wednesday on a security pact with the United States that would enable American forces to stay in Iraq for up to three more years under strict Iraqi oversight.
In the first attack, a bomb attached to a bus used by the Trade Ministry to ferry employees to work exploded shortly before 8am in eastern Baghdad, police and hospital officials said.
Thirteen ministry employees were killed and three were wounded, according to an official with the state-owned Iraqi shopping centres company. The company is part of the Trade Ministry.
The rush-hour attack occurred in a Shiite area and the injured were taken to Kindi and Ibn al-Nafis hospitals in Baghdad.
An official at Kindi hospital's emergency wing and another official at Ibn al-Nafis said eight women were among the 13 people killed. Most of the bodies were severely burned, making identification difficult.
The US military said 14 people were killed and four were injured in the 7.20am bombing of the minibus. It said American soldiers assisted Iraqi police in securing the area and treating casualties.
About 45 minutes later, a female suicide bomber blew herself up as she stood in line to be searched at a checkpoint near the Green Zone in central Baghdad, killing seven people and wounding 13, according to an Interior Ministry official who declined to give his name.
Iraq's intelligence service said the bomber had targeted the checkpoint where its workers enter the Green Zone to go to work at the agency's headquarters, which is inside the fortified area. The service said female employees, including a pregnant woman, were killed and some of its guards were injured.
Kindi hospital said two women were among those killed in the blast.
The US military said the bombing near the Green Zone occurred between 8.30am and 9am and killed two Iraqi army members and three civilians. One civilian was injured, it said.
The Green Zone houses the US Embassy and the Iraqi government headquarters.
In a third attack, a roadside bomb targeted a police patrol around 10.30am near Technology University in eastern Baghdad, killing two civilians and wounding four other people, an Iraqi police officer and an official at Ibn al-Nafis hospital said on condition of anonymity. Two police officers were among the injured.
In Baqouba, 35 miles northeast of Baghdad, a policeman was killed when a roadside bomb blew up near his car, police said.