One of the bombs exploded in a funeral tent where mourners were marking the death two days ago of a Sunni Muslim pro-government militiaman, police said.
It killed 18 people and wounded 16 in Shatub, a village south of Baquba.
Violence has returned to Iraqi capital, two years after U.S. troops left Iraq. Prime Minister Nuri al-Maliki's government said, "The battle will be long and will continue. If we keep silent it means the creation of evil statelets that would wreak havoc with security in the region and the world."
Maliki has ruled out an assault on Falluja by the troops and tanks ringing the city of 300,000, but has told local tribesmen to expel ISIL, which has exploited anger among minority Sunnis against a government they accuse of oppressing them, said a Reuters report.
The country has been witnessing an array of attacks on the public and army by Islamic militants who are trying to carve out a separate state for themselves.
The Baghdad bombings followed attacks that killed at least 24 people the day before, as well as coordinated assaults by militants on a highway bridge and police station near Falluja.
A suicide bomber in an explosives-laden fuel tanker blew it up under the bridge near the town of Saqlawiya, about 10 km (six miles) north of Falluja, causing the bridge to collapse and destroying one of two army tanks parked on top, police said. Gunmen then attacked and destroyed the second tank.