Iraqi Prime Minister Nouri al-Maliki appealed to the country's Shiites and Sunnis to unite to "defeat terrorists and all those who insist on opposing the political process".
A car bomb and mortar attack in the Shiite-dominated and poverty-stricken neighbourhood of Sadr City killed 10 and wounded 51.
Another 23 people were killed, including seven Iraqis executed by gunmen after their bus was ambushed in the Sunni neighbourhood of Ameriyah.
Iraqi and US troops sealed off the capital's Sunni neighbourhood of Dura and state media announced a daytime curfew there from 2pm until 8am, after residents reported hearing gunfire and large numbers of armed men were seen on the streets.
The neighbourhood has been the scene of repeated fighting and attacks on security forces. The whole capital is already under a dusk-to-dawn curfew.
In the northern city of Kirkuk, five people were killed and 19 wounded in a suicide truck bombing, police said.
Monday's attacks come a day after 61 people died in a day of deadly attacks, including a violent rampage by gunmen in which Sunnis were pulled from their cars and killed.
Call for unity
"We have no choice but to defeat those who want to plunge us in the darkness. We can only achieve this through national unity," said Mr Maliki said in an address to the Kurdish regional parliament in the northern city of Arbil.
"We still face a lot of challenges and Iraqi blood is being spilt on our streets every day, but 'no' and a thousand 'nos', they will not defeat us," he said.
Iraq's former Sunni Arab elite accuses militiamen loyal to Shiite parties that lead the national unity government of attacking Sunni civilians in retaliation for insurgent attacks on Shiites.
The latest round of violence comes despite a major security operation in the capital involving over 50,000 troops, forcing the security forces to rethink their security strategies.
US-led coalition forces spokesman Major General William Caldwell said coalition forces, Iraqi security forces and Mr Maliki held talks late on Sunday on the issue or reorganising the forces involved in the plan.
Major General Abdel Aziz Mohammed, the head of the defence ministry's operations room, also admitted there are "gaps" in the security plan.
"The gaps in the implementation of the Baghdad security plan are due to the failure to isolate the terrorists and the persistence of armed groups," he said, referring to militias.
Major General Caldwell also said that illegal armed groups are receiving renewed focus.