The offensive launched at dawn Sunday comes only weeks after Iraqi forces seized second city Mosul from IS.
The offensive launched at dawn Sunday comes only weeks after Iraqi forces seized second city Mosul from IS and as the jihadists also face assaults on their positions in Syria.
Tal Afar was once a major supply hub between Mosul and the Syrian border and capturing it would be another major blow to IS's self-declared "caliphate" that once controlled large parts of Syria and Iraq.
The Iraqi army, federal police and counter-terrorism forces backed by 20,000 fighters from the Hashed al-Shaabi paramilitary group launched the offensive on Tal Afar.
They are battling IS on three fronts -- the west, south and southeast -- and commanders have told AFP they expect to tighten the noose on the jihadists by edging closer to the gates of the city.
The federal police said its forces had retaken four villages on the western front on the first day of the operation while the Iran-backed Hashed said its fighters had advanced to the edges of Tal Afar's western suburbs.
Iraqi forces have been pounding IS with mortar fire after weeks of air strikes to weaken the fighters who overran Tal Afar in 2014.
In an indication of their next target, Iraqi planes on Sunday and Monday dropped leaflets on the town of Hawijah to the south, urging residents to prepare as "retaking your city is the next goal of the armed forces".
Hawijah in Kirkuk province is some 300 kilometres (185 miles) northwest of Baghdad.
The jihadists also still hold areas of the vast western desert province of Anbar, including the Al-Qaim area on the border with war-ravaged Syria.
The battle for Tal Afar, the last major population centre in northern Iraq under jihadist control, has sparked fears for thousands of civilians trapped inside.
The US-led coalition fighting IS in Iraq and Syria says between 10,000 and 50,000 civilians are estimated to be in and around Tal Afar.
UN Humanitarian Coordinator for Iraq Lisa Grande said Sunday that "more than 30,000 people have already fled" the Tal Afar region and that thousands more were expected to follow.
"Families are trekking for 10 to 20 hours in extreme heat to reach mustering points. They are arriving exhausted and dehydrated," Grande said in a statement.
"We don't know how many civilians are still in the areas where fighting is occurring, but we are preparing for thousands more to flee in coming days and weeks."
When IS captured Tal Afar, the population was estimated at around 200,000 and was overwhelmingly Turkmen, one of Iraq's largest ethnic minorities.
Prime Minister Haider al-Abadi announced the Tal Afar offensive in a pre-dawn televised speech Sunday, warning IS jihadists that they had "no choice other than to leave or be killed".
"We have won all our battles, and Daesh have always lost," he said, wearing black military fatigues and using an Arabic name for the group.
The US-led coalition welcomed the start of the assault and pledged its continued support for Iraqi forces battling the jihadists.
The "operation to liberate Tal Afar is another important fight that must be won to ensure the country and its citizens are finally free of ISIS", the head of the anti-IS coalition Lieutenant General Stephen Townsend said in a statement, using another acronym for IS.