"This ... [operation] clearly indicates that the military campaign has further dimensions than those announced, and that its goal is to crack down on the sons of this governorate [of Mosul] who reject the occupation and its allies, a statement said.
"The AMS denounces this brutal operation which aims to liquidate all the city's people who reject the occupiers and their destructive plans."
Nizar Fahmy, a journalist working in Mosul, told Al Jazeera that the situation on the ground has deteriorated during the operation, to a degree where residents are struggling to obtain basic necessities.
The city is under curfew, with only pedestrians allowed out onto the streets during the day.
He said: "People have resorted to getting vegetables and fruit from the outskirts of the city - where the first checkpoint leading to Mosul is.
"Merchants have been forced to resort to peddling their wares on carts, as they travel to different neighbourhoods."
Fahmy also said that security forces have constructed a list of names of so-called "suspects" that are wanted and are conducting house-to house searches based on this list.
Al-Qaeda fighters are said to have regrouped in Mosul and the surrounding province of Nineveh after being pushed out of Baghdad, the Iraqi capital, and western Anbar province by US and Iraqi forces.
It is unclear how long al-Maliki will stay in Mosul, but his visit is similar to his trip to the southern city of Basra in late March when he oversaw a military operation against fighters loyal to Muqtada al-Sadr, a populist Shia leader.
Iraqi security forces backed by the US military launched a "new phase" of operations on Saturday in Nineveh province, which borders Syria and Turkey, the US military said.
In February, al-Maliki had announced plans for an operation against al-Qaeda and called on the population to support the security forces to get rid of "terrorists".
On Monday, he told parliament his troops had only begun preparatory operations and that a major operation was yet to come.
He said: "When this phase of preparation is completed, we will announce the start of the military offensive".
Mosul, the capital of Nineveh, 370km north of Baghdad, has been described by the US military as the centre of the fight against al-Qaeda.
The city, one of the most dangerous places in the country, has been the scene of many bombings and attacks.
On January 23, an explosion at an ammunition dump killed more than 60 people and destroyed dozens of homes.
Nineveh's police chief was killed in a suicide bombing when he visited the site of the explosion on the following day.