Officials said insurgents first detonated a car bomb around noon in the parking lot of Taji's local council building. When civilians and security forces rushed to the scene to help the victims, the second bomb was detonated.
Burned bodies were lying on the ground and about 20 cars were on fire, witnesses said.
The bombing follows a late night rocket attack on Baghdad's heavily fortified Green Zone. Four Iraqis were killed and another 10 were wounded. It hit while Americans were celebrating the Fourth of July at the U.S. embassy in the Green Zone.
The explosions in Taji, a Sunni-dominated town about 12 miles north of Baghdad, are the latest in a series of attacks across Iraq as the government and political leaders debate whether to ask the United States to keep some American troops there past their year-end withdrawal deadline from the country.
Vice President President Tariq al-Hashemi, a Sunni politician, demanded that Shiite Prime Minister Nouri al-Maliki quickly appoint defense and interior ministers to help deal with growing chaos among the security forces. The two senior posts have been vacant for more than six months as government officials squabble over which parties should hold them. "The security system needs to be or fixed as soon as possible," al-Hashemi said.
Parliament Speaker Osama al-Nujaifi, another Sunni, lashed out security forces, saying they are not doing enough to foil such attacks.
While violence in Iraq is less intense now than during Shiite-Sunni sectarian fighting in 2006 and 2007, militants have again stepped up deadly attacks. That has prompted concerns about what will happen when the 47,000 remaining U.S. troops pull out.
The Associated Press contributed to this report.