Two car bombs exploded in southern Baghdad, killing six people and wounding 15, China's state-run news agency Xinhua reported.
Another car bomb went off near a group of day laborers in the southeastern part of the capital, killing four and wounding 15 others, police said.
Others were killed in bombings at a parking lot near a court complex and a market.
Baghdad and other areas of Iraq have been wracked by violence in recent months. Hundreds of people have been killed.
Prime Minister Nouri al-Maliki, in a speech in Nasiriyah Sunday, blamed "treacherous" Arab countries for the surge in violence, the Middle East News Agency reported.
"Iraq is the target for some countries that are backing terrorism, and backing evil," Maliki said "The world has united with us. The [U.N.] Security Council, the European Union and most Arab countries, except some diabolical treacherous countries."
Maliki warned that countries backing violence in Iraq also would suffer, arguing "this evil has started to expand and it will reach those same countries, as it reached others previously."
An audio message posted online urged anti-government fighters in a standoff with Iraqi forces in Anbar province to "creep toward Baghdad," MENA said.
The remark, reportedly from the leader of the Islamic State of Iraq and the Levant, urged anti-government fighters not to "waste" the opportunity to advance, the news agency said.
"Sons of the [Islamic] state in Iraq, you are stronger than a mountain," said a voice MENA said apparently was that of Abu Bakr al-Baghdadi in an address to Sunni Arabs.
"Be the spearhead in fighting the Safavids, stay on the front line and creep toward Baghdad and to the south," he said, using negative terms for Iraq's Shiite majority.
The fighting erupted in Ramadi Dec. 30, when security forces cleared a Sunni Arab protest camp and then spread to Fallujah. Militants moved in and seized Fallujah and parts of Ramadi after security forces withdrew.