If confirmed, that would mark a significant advance by the Ninth Armoured Division, which had been tied up for more than a month in close-quarter combat with Islamic State on the southeastern fringes of the city.
Residents of Islamic State-controlled districts of east Mosul said by telephone the army had punched deep into the east bank of the city, getting close to the Tigris.
"The fighting right now is very heavy - Iraqi forces have gone past our neighborhood without entering it. Our area is now practically surrounded by the river and the Iraqi forces," said a resident of the Palestine neighborhood.
Islamic State's news agency appeared to confirm the advance, saying three car bombers struck the troops near Salam hospital.
A Reuters team saw thick black smoke rising from the area around the hospital. "We made good advances today," said a soldier who identified himself as Abu Ahmed.
Mosul is by far the largest city under Islamic State control and defeat there would roll back the self-styled caliphate it declared in 2014 after seizing large parts of Iraq and Syria.
Some 100,000 Iraqi soldiers, security forces, Kurdish peshmerga fighters and mainly Shi'ite paramilitary forces are participating in the Mosul campaign that began on Oct. 17, with air and ground support from a U.S.-led coalition.
A colonel in the armored division said December 6's assault, launched at 6 a.m., aimed to ultimately reach Mosul's Fourth Bridge, the southernmost of five bridges spanning the river.
The bridge, like three others, has been hit by U.S.-led air strikes to prevent Islamic State sending reinforcements and suicide car bombs across the city to the eastern front.
The last and oldest bridge, built in the 1930s, was targeted on December 5 night, two residents said. The structure was not destroyed, but the air strikes made two large craters in the approach roads on both sides.
"I saw Daesh (Islamic State) using bulldozers to fill the craters with sand and by midday vehicles managed to cross the bridge normally. I drove my car to the other side of the bridge and saw also Daesh vehicles crossing," a taxi driver told Reuters.
