The attacks bring the toll to more than 140 people killed in just seven days in and near Baghdad.
The unrest highlights significant flaws in Baghdad security procedures that have gone largely unaddressed even as US-led forces train their Iraqi counterparts for the fight against the Islamic State (IS) group.
The deadliest attack hit the Sadr City area in northern Baghdad, where a suicide bomber detonated an explosives-rigged vehicle, killing at least 21 people, security and medical officials said.
Another attack hit the Shaab area, also in northern Baghdad, killing at least 15.
Interior ministry spokesman Saad Maan said it was carried out by a female suicide bomber, while a police colonel said there was a roadside bombing followed by the suicide attack.
But IS issued a statement claiming the attack, which it said was carried out by a man identified as Abu Khattab al-Iraqi. The bomber threw hand grenades and then detonated a suicide belt, IS said.
Attacks by female suicide bombers are rare in Iraq, though they were once more common.Two mentally disabled women wearing suicide vests killed nearly 100 people at Baghdad pet markets in early 2008.
Two women also detonated explosives at one of the country’s holiest Shiite sites the following year, killing more than 60 people, while a 2010 attack on Shiite pilgrims by a female bomber left over 40 dead.
– Baghdad security flaws – In a third attack in the Iraqi capital on Tuesday, a car bombing in the Rashid area of southern Baghdad killed at least three people, officials said.
The Baghdad attacks also wounded a total of more than 100 people on Tuesday. There was no immediate claim of responsibility for the attacks in Rashid and Sadr City, but IS has claimed a series of other attacks in and near Baghdad that have killed more than 100 people in seven days.
The terrorists carried out triple car bombings in northern Baghdad that killed at least 94 people, and a further 12 died in attacks on a police station west of the capital and a gas plant to its north.
Attacks in the city decreased following a June 2014 IS offensive that saw its fighters focus on holding territory and fighting battles in other areas, and large quantities of explosives used in areas outside Baghdad.
But Iraqi forces have regained significant ground from IS, and the frequency of attacks in the capital has increased in recent weeks.
While thousands of Iraqi security personnel have been trained by US-led coalition forces to fight IS, major security flaws persist in Baghdad. Fake bomb detectors are still in widespread use across the city despite the fact that the man who sold them to Iraq was sentenced to jail for fraud three years ago.
And while checkpoints around the capital cause major traffic jams, they have a questionable impact on security, as checks of document and searches of vehicles are cursory if they take place at all.