The first bombing at 6.15am (0215 GMT) on Monday targeted the Sadir hotel in central Baghdad, which is used by foreign security personnel.
A bomber blew up a minivan packed with explosives at a checkpoint at the gates to the hotel – which has been bombed in the past – killing six people and wounding 16, Iraqi journalist Walid Khalid told Aljazeera.
Witnesses said the explosion was followed by the sound of automatic weapons fire.
Most of the casualties were Iraqi private security guards employed by the hotel.
At 8.30am (0430 GMT), a car bomb targeted a police commando patrol under the Harithiya bridge in the west of the city, killing three policemen and wounding 11, Khalid added.
Also on Monday, armed men killed a family of four as they waited on the street for a ride in the city of Samarra, 95km north of Baghdad.
Police said Subhi Thamir Husayn al-Badri, his wife and two sons were shot dead in the Jiriya district, adding that the reason for the killing was unclear.
US soldier killed
A US soldier was also killed on Monday near Samarra, north of Baghdad.
The US military said in a statement the soldier died “when an improvised explosive device detonated near his vehicle during a combat patrol.”
The death of the solider brings the total number of US military personnel, who have died in Iraq since the March 2003 invasion, to 1768.
In another development, about 150 doctors at Iraq’s largest hospital complex staged a protest on Monday against colleagues being abused by security personnel.
The doctors at Medical City, a complex of four hospitals in the capital, withdrew non-emergency cover on Monday, after a group of Iraqi police angry at the death of a colleague assaulted a doctor and other hospital staff.
Doctors are protesting but still
“The officer died despite our attempts to save him and, hearing this, the policemen beat our doctor, Muhammad Jalal, who told them about the death,” Dr Rafid al-Hassani said.
Al-Hassani said the protest was being supported by 150 of the complex’s 1250 doctors.
“Other doctors are continuing to work as we are carrying out emergency as well as routine hospital services. But we are striking as we want security.”
Al-Hassani said the angry policemen had also broken some medical equipment, beds and other furniture during Sunday’s scuffle with the staff.
Another hospital source said that Medical City was unable to take any emergency cases on Monday as its casualty unit had been damaged in the disturbance and a back-up facility was still under construction.
It was the second time in six days that the hospital staff had withdrawn non-emergency cover in protest at abuses by Iraqi security personnel.
Last Tuesday, 40 medics at the capital’s Yarmuk hospital launched a work to rule to protest at an assault against two doctors and other staff by Iraqi troops.