Iraqi special forces are now less than 1.5km from the eastern outskirts of Mosul and are preparing to enter the city held by Islamic State fighters.
Hundreds of Counter-Terrorism Service (CTS) troops entered Bazwaya, the last village before the city limits, after launching a dawn assault on Monday.
A BBC correspondent travelling with them says there was some resistance, with car bombs targeting the convoy.
Units of the army’s ninth division are meanwhile advancing from the south.
Earlier, the military announced the start of an operation to retake Mosul’s “left bank”, a reference to the eastern side of the River Tigris, which flows through the city from north to south.
Hundreds of troops in heavily-armoured Humvees, together with tanks and bulldozers, advanced on the village, supported by US-led coalition air strikes, our correspondent adds.
Within hours the head of the Iraqi military’s Nineveh Operations Command, Lt-Gen Abdul Amir Yarallah, announced that they had entered Bazwaya and raised the Iraqi flag.
Our correspondent says that a column of troops is now probing different parts of Mosul’s outskirts, as commanders make a plan about where to go next.
One senior officer told the Associated Press news agency that they aimed to enter the city limits later on Monday, while another told Reuters they were already fighting in the Karama district.
CTS commander Lt Gen Abdul Wahhab al-Saidi denied that the troops had entered Karama. But he did say that they were moving on Kokajili, an industrial zone west of Bazwaya that lies about 1km from Mosul’s municipal boundary.
It had been expected the CTS would halt its advance until troops and allied fighters on other frontlines also reached the outskirts of Mosul.