According to Reuters, Iraqi television quoted operations commander Lieutenant-General Abdul Ameer Rasheed Yarallah as saying troops had entered the Salam Hospital in the southeastern neighborhood of Wahda, close to the river.
An army colonel told Reuters the offensive, backed by fresh reinforcements and launched at 6 a.m. on Tuesday, aimed to overwhelm Islamic State militants who have been waging fierce counter attacks against the army in the east of the city.
The fierce urban warfare has slowed advances by the army's elite Counter Terrorism Services in the east of the city, and the army's Ninth Armored Division in the southeast.
"We are using a new tactic - increasing the numbers of advancing forces and also attacking from multiple fronts to take the initiative and prevent Daesh (Islamic State) fighters from organizing any counter-attacks," the colonel said by telephone.
The troops are part of a 100,000-strong Western-backed coalition of Iraqi soldiers, security forces, Kurdish peshmerga fighters and mainly Shi'ite paramilitary forces that launched the attack on Islamic State's stronghold in Iraq seven weeks ago.