With the crucial battle in its second day, Iraqi commanders said progress was being made as fighters pushed on two main fronts towards the city.
The US military, which is leading a coalition providing air and ground support, said Iraqi forces even looked "ahead of schedule" but warned the battle would be long and difficult.
Advancing in armoured convoys on several fronts across the dusty plains surrounding Mosul, forces moved into villages defended by pockets of IS fighters after intensive aerial bombardment.
Massive columns of smoke rose from burning oil wells near the government forces' main staging base in Qayyarah, blotting out the horizon and turning the sky grey for miles.
A soldier at a checkpoint nearby said that IS lit the wells on fire to provide cover from air strikes before the town of Qayyarah was retaken in late August. The fires had been burning ever since.
The long-awaited offensive was launched on Monday, with some 30,000 federal forces involved in Iraq's largest military operation since the 2011 pullout of US troops.
Retaking Mosul would deprive IS of the last major Iraqi city under its control, dealing a fatal blow to the "caliphate" the jihadists declared two years ago after seizing large parts of Iraq and neighbouring Syria.
Iraqi commanders said IS fighters were hitting back with suicide car bomb attacks but that the offensive was going as planned.
"Many villages have already been liberated," said Sabah al-Numan, the spokesman of the elite counter-terrorism service.
"Iraqi forces have achieved their goals and even more, but we're careful to stick to the plan and not rush this."
'Difficult campaign' ahead
The two main fronts are south of Mosul, where forces are moving from Qayyarah, and east, where another push involving Kurdish peshmerga fighters is under way.
In the south, forces inching forward along the Tigris river were training their sights on a village called Hammam al-Alil, while units east of Mosul were close to Qaraqosh, once Iraq's biggest Christian town.
Iraqi forces have significant ground to cover before reaching the boundaries of the city, which IS is defending with berms, bombs and burning oil trenches.
A siege is likely to ensue and then a breach by crack units that will engage die-hard IS fighters.
IS forces are vastly outnumbered, with the US military estimating 3,000 to 4,500 jihadists in and around Mosul.
"Our forces are using a variety of means at their disposal against the terrorists and we'll have more surprises for them when we reach the city," Numan told AFP.
The US-led coalition said strikes destroyed 52 targets on the first day of the operation.
"Early indications are that Iraqi forces have met their objectives so far, and that they are ahead of schedule for this first day," Pentagon press secretary Peter Cook said.
"We are in the first day of what we assume will be a difficult campaign that could take some time."
Aid groups are bracing for a potentially massive humanitarian crisis.
Fears of civilian exodus
The United Nations' humanitarian coordinator, Lise Grande, said on Monday that few civilians were as yet fleeing Mosul but that a major exodus could begin in the coming days.
Mosul is Iraq's second-largest city and the UN fears that up to a million people could be forced from their homes by the fighting, 700,000 of them in need of shelter.
"Humanitarian partners are focusing on preparing shelter in three priority areas south of Mosul where the first displaced families from Mosul will be accommodated," it said.
Mosul is a cornerstone of IS's bid to create a jihadist state, an unprecedented experiment that now appears to be crumbling.
One of the main challenges of the Mosul operation is to bring the area's myriad forces and political players together.
Iraqi military and police forces have been joined on the battlefront by an array of sometimes rival forces, including the Kurdish peshmerga, Sunni tribal fighters and Iran-backed Shiite militia.
Iraqi Prime Minister Haider al-Abadi's relations with the Kurds, who control vast areas around Mosul, have been tense in recent months.
But the autonomous northern region's leader, Massud Barzani, on Monday hailed the two sides' cooperation in the fight.
Barzani is a close ally of neighbouring Turkey, whose president Recep Tayyip Erdogan made clear Monday he wanted his forces to be involved in the operation.

Source: AFP
Turkish jets
Prime Minister Binali Yildirim said Tuesday that Turkish jets had taken part in the campaign, without giving further details.
Turkey has troops stationed north of Mosul and Erdogan's statement angered some Iraqi nationalists who staged a demonstration in Baghdad on Tuesday.
A high-ranking Turkish delegation was holding talks with official in Baghdad Tuesday.
IS once controlled more than a third of Iraq's territory but its self-proclaimed "state" has been shrinking steadily.
If Mosul falls, only Raqa in Syria would remain as the last major city in either country under IS control.
But even the recapture of Mosul will not mark the end of the war against IS, which is likely to increasingly turn to insurgent tactics as it loses more ground.
Just hours after the offensive began, IS claimed responsibility for a suicide car bombing targeting an Iraqi army checkpoint south of Baghdad that killed at least 10 people.
IS has also organised or inspired a wave of attacks in Western cities and on Tuesday the European Union's security commissioner raised concerns over the potential impact of Mosul's fall.
"The retaking of the IS' northern Iraq stronghold, Mosul, may lead to the return to Europe of violent IS fighters," Julian King told German daily Die Welt.
He said even a handful of jihadists returning would pose a "serious threat that we must prepare ourselves for."