"After every defeat Isis receives at the front, in the actual war, they launch an attack on Baghdad," he added.
In a statement circulated online, the militant group warned of "worse to come".
Last month, it lost its grip on the town of Hit, in the western province of Anbar. To the north, security forces have been preparing for an attack on Mosul.
On Tuesday, James Clapper, the US director of national intelligence, said in a Washington Post interview that efforts by the United States and Iraq to retake Mosul "will take a long time and be very messy".
"I don't see it happening in this Administration," Clapper said.
The bombings also come at a time of political turmoil in Baghdad. Today, politicians and security officials traded blame for the violence.
The worst attack occurred in one of the busiest markets in Sadr City, a neighbourhood that is a major support base for Shia cleric Moqtada al-Sadr. Sadr has led calls for political reform, including firing Iraq's ministers and replacing them with technocrats.
His followers dramatically breached Baghdad's fortified Green Zone late last month and ransacked Parliament.
Residents of Sadr City took to the streets after the bombings, directing their frustration at the Government and security forces.
"We already had a lot of anger, that's why we stormed the Green Zone," said Karrar Ali, a 35-year-old lawyer from Sadr City. "Now people are more angry and blame the government for failing to protect them."
Ali, who said he arrived at the bomb site about half an hour after the attack, said he was met with a "terrifying scene".
"There was smoke fire, human flesh," he said. "Everyone was in a state of confusion."
In a gruesome yet familiar scene, witnesses described how wooden market carts were used to carry the dead and injured after the bombing.
The Shia neighbourhood in eastern Baghdad has suffered two other large-scale market bombings in the past year, killing a total of 140 people. Isis, a Sunni group, considers Shia Muslims to be apostates.
"The market was so crowded," said Haider Salah, 28, a taxi driver who witnessed the attack. "At that time of the morning, the market is filled with women and their children."
Just hours after the market blast, an explosion occurred at a checkpoint on the outskirts of the Shia neighbourhood of Kadhimiyah in the north of the city.
A man wearing a suicide belt detonated the explosives at a point where civilians are searched as they enter the neighbourhood, killing two police officers and four others, according to the Baghdad Operations Command.
A third suicide attack followed at a checkpoint on a road that leads to Kadhimiyah, indicating that the neighbourhood, home to Baghdad's most important Shia shrine, was probably the intended target.