Three civilians were killed and eight others injured after a car bomb targeting a US patrol exploded in the central Baghdad district of Mansour.
The US military said two of its soldiers were among the injured.
Police colonel Abdulmajid Mohammed was killed after a bomb planted under his car exploded as he drove to work in al-Zubair.
His driver, also a police officer, survived the explosion but was said to be in a critical condition in hospital.
In another attack, Ammar Aziz Mohammed Ali, the deputy higher education minister, survived an assassination attempt in Baghdad.
"A roadside bomb blew up as the ... minister's convoy was passing down al-Nidhal Street in central Baghdad without hurting him," a government-issued statement said.
Two civilians and two police officers were wounded by the blast, according to an interior ministry source.
Estate agent shot
Also on Tuesday, Iraqi police said a real-estate agent was shot dead after unknown assailants opened fire on his office in the city of Mosul, which lies around 370km north of Baghdad.
Another police officer was left wounded after security forces opened fire on a suspected suicide bomber who refused to stop as he approached a police checkpoint.
The police said it was unclear if the explosion was a result of gunfire from security forces or if the driver had detonated any explosive devices.
The string of attacks came on the same day that Barack Obama was sworn in as the new US president in a ceremony held in the US capital Washington DC
In his inauguration speech, Obama pledged to "begin to responsibly leave Iraq to its people" and to forge a new relationship with "the Muslim world ... based on mutual interest and respect".
While attacks had fallen across Iraq in recent months, many security sources believe there will be a surge in violence in the run-up to provincial elections due to be held on January 31.