The American military also said five US troops died in separate attacks.
The first blast occurred at 5pm on Thursday, when a car bomb detonated near a gas station, killing at least two people and wounding 13, police Major Falah al-Mohammedawi said.
The second, believed to be driven by a suicide bomber, went off 20 minutes later in a bustling outdoor market, killing nine people and wounding 57, said al-Mohammedawi.
The US military said the five American troops died on Wednesday in separate attacks.
A roadside bomb blast killed three US soldiers south of Baghdad, while a fourth soldier died from wounds suffered in a small-arms fire attack in the capital's southwest, the military said.
A US marine was fatally wounded during combat near the western city of Falluja.
The deaths were the first of US personnel reported since 28 January and took the total of US military deaths to 2247 since the Iraq war began in March 2003, according to an Associated Press count.
A US marine was fatally wounded
during combat in Falluja
Also on Thursday, a shepherd found the partially buried bodies of 16 men on the eastern outskirts of Baghdad, each of whom had been shot multiple times, bound and blindfolded, police said.
All the victims appeared be aged between 30-40 years, wore civilian clothes and had no identity documents.
Also on Thursday, a US helicopter fired a rocket at a house in the Shia district of Sadr City after being shot at, the US command said.
The rocket damaged several houses, killing a young woman, residents reported. Shia politicians condemned the incident as reckless and provocative.
The US military said the exchange of fire took place at about 1am as US troops were pursuing a "known terrorist associated with Ansar al-Sunnah", a Sunni militant group that has claimed responsibility for numerous suicide attacks and beheadings.
US soldiers also detained two unidentified people before the attack inside Sadr City, the power base of Shia cleric Muqtada al-Sadr.
"These military operations... are considered provocative and represent a clear violation against the security situation in the country"
Iraqi transport minister
Salam al-Maliki, Iraq's transport minister, condemned the US attack and demanded compensation for victims.
Al-Maliki said: "These military operations aim at weakening the supporters of the Sadrist movement, are considered provocative and represent a clear violation against the security situation in the country."
Attacks continued on Thursday with two roadside bomb blasts targeting an American patrol and damaging two Humvees in Tarmiyah, 50km north of Baghdad, police Lieutenant Ali al-Bayati said.
The US military said there were no American casualties.
Another roadside bomb blast killed three Iraqi Army soldiers in eastern Baghdad's Ghazaliyah neighbourhood, said army Major Moussa Abdul Karim.
Insurgents fired three mortar rounds at the Oil Concentrating Complex, 45km west of Kirkuk, triggering a fire but causing no casualties, police Captain Farhad Talabani said.
US troops sealed off the site as firefighters struggled to extinguish the blaze.
Insurgents routinely target local security forces and oil installations in a bid to cripple US-led attempts to rebuild the post-Saddam Hussein Iraq following the 2003 US-led invasion.