Among the wounded were 25 Iraqi soldiers and five civilians, he said.
In a separate incident on Sunday, armed men in three cars opened fire on pedestrians in southern Baghdad, police said, killing at least seven people and wounding 16 others.
There were few details of the shooting, which took place in Zaafariniya, a religiously mixed neighbourhood.
In another attack in the Iraqi capital, a Katyusha rocket struck a residential building in the eastern Al-Kamaliyah neighbourhood, killing at least five people and wounding eight, security officials said.
A car bomb near a bus stop in Baghdad's al-Shuala neighbourhood, meanwhile, killed five people and wounded eight others, security officials said.
Further north, a roadside bomb near the town of Al-Tuz, 75km south of Kirkuk, killed four Iraqi army personnel, a medic said.
The US military, meanwhile, said its troops raided a "suicide bombing network" in Diyala province northeast of the capital, killing 12 men.
Elsewhere in Iraq, four people, including a police officer, were killed in shootings, police said.
Green Zone attack
The day's violence began when the heavily fortified Green Zone inside the Iraqi capital was targeted by two waves of mortar attacks.
There were no reports of casualties but at least 10 blasts were heard in the area in central Baghdad, starting shortly before 6am on Sunday, while helicopters were seen circling overhead.
The 10sq km zone is located on the west bank of the Tigris river that bisects Baghdad.
It houses the US and British embassies, the Iraqi government headquarters and thousands of American troops.
There were no claims of responsibility for the attacks. But it appeared the rounds were fired from areas of eastern Baghdad where the Mahdi Army of Muqtada al-Sadr, the biggest Shia militia, operates.
Last month, the US military blamed what it calls Iranian-backed armed Shia groups for a series of deadly rocket attacks in Baghdad.
Those included one that struck Camp Victory, the main US military headquarters, and an Iraqi housing complex on the capital's southwestern outskirts on February 18, killing at least five people and wounding 16 more, including two US soldiers.
US troop deaths
The attacks in Mosul and Baghdad come a day after the US military announced the deaths of four soldiers in Iraq, including three in a single roadside bombing in Baghdad.
A US soldier also died from injuries on Saturday sustained during a gun battle the previous day.
Separately, in Baghdad's southern al-Amel neighbourhood, five Iraqis were injured during clashes between the Mahdi Army on the one hand and US and Iraqi forces on the other.
Also on Saturday, Iraqi police reported the deaths of six Iraqis after a US Apache helicopter struck two checkpoints near the central city of Samarra. Two Iraqis were wounded during the attacks.
Abu Faruq, leader of an Awakening Council unit allied with US forces against al-Qaeda in Iraq, said the six Iraqis were members of his group who had been manning the checkpoints when they came under attack.