Nearly 70 people were hurt in the blasts, which targeted Shiite pilgrims taking part in the commemoration of a revered imam on the city's northwest side.
At the time of Saturday's attacks, roads had been closed and the army and police had been deployed to protect thousands of pilgrims marking the martyrdom of an eighth-century imam, Musa Kadhim, The New York Times reported.
A parked car exploded in the Kadhimiya area of Baghdad, near a shrine that is the focal point of the festival of the imam, killing at least 18 people and wounding 35, an Interior Ministry official said.
In the other attack, a suicide bomber exploded his car on a highway leading northwest from Baghdad, killing 14 and wounding at least 32, a security official said.
Khalad Fadhel, a military analyst, said security officials over-emphasized deploying large numbers of soldiers and police officers without focusing enough on intelligence work to detect terrorist plots.
"It shouldn't be a military parade," Mr. Fadhel said. "We need a security strategy that addresses these shortcomings. I think that what we've really missed after the withdrawal of the United States is intelligence information. They were good providers of this kind of information about possible attacks."
CNN said violence between Shiites and Sunni Muslims has been on the wane since U.S. troops wound down their presence in Iraq. However, some Sunni hard-liners continue to carry out terrorist attacks. Sunnis dominated the regime of Saddam Hussein prior to his ouster by U.S. troops in 2003.
No one immediately took responsibility for Saturday's attacks, which followed a wave of bombings targeting Shiite pilgrims that left 93 dead.
The terrorist group al-Qaida claimed it was behind Wednesday's bombings. A statement posted on the Internet said the attacks were retaliation for the supposed confiscation of Sunni lands and mosques by the government. Alsumaria Iraq Television said the statement alleged Iraq's Shiites were allied with Iran to impose "a new reality in the country."