He denied security forces had shot directly at protesters.
As a group of Iraqi journalists were interviewing another protester in the square, a policeman opened fire and wounded the youth in the leg.
On Saturday, Prime Minister Adel Abdul-Mahdi launched measures to appease the demonstrators, such as paying unemployment benefits and providing subsidized housing for the poor.
He said his forces would support actions against corrupt institutions but not "the fall of the regime", a chant which has featured more prominently in the protests in recent days.
The military said early on Monday it was withdrawing from Sadr City and handing over to police in an apparent effort to de-escalate tension there.
Clashes between police and protesters killed 11 people in Baghdad on Saturday in a new flare-up of anti-government unrest, as security forces deployed in their hundreds to keep demonstrations away from central squares in the Iraqi capital. The deaths in Sadr city added to a toll of more than 100 people killed since the protests began.
Iraqi Prime Minister Adel Abdul-Mahdi ordered police to replace the army in Sadr City, the Shiite-dominated neighborhood east of the Iraqi capital.
"I am ready to go wherever our brotherly protesters are and meet them or send them envoys to other locations without any armed forces", he said.
The military said all members of the security forces who "acted wrongly" will be held accountable.
In a news conference broadcast on state television, Maan also said that authorities condemned all attacks against media outlets, after reports of raids at the offices of several local and global news outlets by unidentified groups.
Rasoul Saray, a 34-year-old unemployed Baghdad resident who wore a green mask, vowed to continue protesting despite the crackdown.
A Sadr City resident reached by phone told Reuters that the streets were calm during the day. Troops blocked the main road preventing them from advancing and fired above the protesters' heads. Ducking, the protesters piled over one another taking cover behind a short wall.
Meanwhile, Abdul-Mahdi pledged to meet with the demonstrators to hear their demands.
The renewed violence came hours after the government announced a string of reforms following an "extraordinary" session overnight in response to the protests that began on Tuesday.
Across Baghdad on Monday morning as in several southern cities, streets were reopening and no protests could be seen, although demonstrators typically gather in the late evening.
It is the deadliest unrest since the Islamic State (IS) terror group was declared defeated in Iraq in 2017. The Speaker of the Parliament Salim al-Jabouri then issued a statement backing the protestors.
"We call on the people of Iraq to show further self-restraint and seek democratic and legal solutions for addressing their demands".