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 the side of Mosul east of the River Tigris, which flows through the city.
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The BBC’s Ian Pannell, who is with a CTS unit, says the assault on Bazwaya, about 3km (1.9 miles) from Mosul, began early on Monday.
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.
Life under IS – by Rakan Jauid Aid
When Daesh (a term for IS) entered Mosul, they killed my father because he was a police officer. I got away – they didn’t come after me.
My village was besieged for two years and a couple of months. If I had spoken to anyone about being in the police or army, Daesh would have killed me.
It happened to many of my close friends. They would go to their homes and Daesh would just take them away.
Daesh are just beards. They force you to attend all the prayers at the mosque. If your woman is not wearing a hijab, they will whip you – they have complete control.
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 Kukjali, 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.
Gen Yarallah announced earlier that the army’s ninth division had taken control of the village of Ellag, 17km (10 miles) south of Mosul.
Army units also recaptured a number of villages to the south-east and north, the military said, while federal police are moving north from the town of Shura towards Hamam al-Alil.
About 50,000 Iraqi security forces personnel, Kurdish Peshmerga fighters, Sunni Arab tribesmen and Shia militiamen are involved in the two-week-old offensive to drive IS militants out of their last major urban stronghold in the country.
Mosul fell to the jihadists in June 2014 and their leader, Abu Bakr al-Baghdadi, chose a mosque in the city as a place to proclaim the establishment of a “caliphate”.
Before the offensive began on 17 October, there were believed to be between 3,000 and 5,000 militants remaining in Mosul, along with up to 1.5 million civilians.
More than 17,700 residents have fled so far and, according to the UN’s worst-case scenario, as many as 700,000 others could follow suit.
Mosul battle: Iraqi forces near city’s eastern outskirts}