In the deadliest attack, 11 people were killed at a Shi'ite mosque in north Baghdad, where a bomb planted in a motorcycle went off outside as worshippers were leaving following late night prayers, the defence ministry said.
An Iraqi military commander said a spate of 600 attacks had killed nearly 100 people in the past week.
"We've noticed an increase in terrorist attacks in the last three days after the formation of the new government," said Major General Abdel Aziz Mohammed, commander of the defence ministry's operations room.
General Mohammed said 98 civilians had been killed and 280 wounded in 607 attacks in the week to Monday.
Around 85 suspected insurgents were killed by coalition and Iraqi forces in the same period, he added.
A United Nations report said nearly 2,500 people been killed in March and April and 85,000 had fled their homes.
US ambassador Zalmay Khalilzad acknowledged that parts of Iraq were out of the control of government troops and their coalition allies.
"Parts of Anbar are under control of terrorists and insurgents," he told CNN, referring to an overwhelmingly Sunni Arab province west of the capital, which was one of the first strongholds of the insurgency.
In other violence, a car bomb exploded at a market in the Baghdad Shi’ite neighborhood of Sadr City, killing five people, police said.
In the main northern city of Mosul, a family was targeted when gunmen drove up next to their car and opened fire, killing four people and wounding one, police said.
The latest bloodshed underscores the urgency to fill three government security posts, and a Shi'ite politician close to Prime Minister Nouri al-Maliki said that the vacant slots of defence and interior minister would be filled within the next two days.
Mr Maliki's cabinet, approved by parliament on Saturday, still lacks the two ministers and one security chief charged with reining in insurgent and sectarian violence.
Parliament agreed to approve Mr Maliki's government after the premier promised to staff the posts within a week.
Four names are under consideration for the interior ministry. Among them are former national security advisor Muwaffaq al-Rubaie, a former army general and an inspector general in the ministry, the source close to Mr Maliki said.
Prominent politician Ahmed Chalabi has been dropped from the shortlist, and independent Shi'ite politician Qassem Dawud is being considered for the post of minister of state for national security.
Four names have also been put forward for defence.
They include former parliament speaker Hajem al-Hassani and Thamer Sultan al-Tikriti, an army general who was imprisoned under the old regime and whose brother was executed by Saddam Hussein, as well as another former general.
The promise to fill the posts came a day after Iraqi leaders renewed pledges to take over more military responsibility from foreign forces amid mounting public pressure in the United States and Britain for troop reductions in Iraq.