He says other reports indicate displaced people from Tal Afar are being harassed and subjected to revenge attacks.
"ISIS' days are certainly numbered, but it is not over yet and it is not going to be over anytime soon", Mattis told reporters in Amman.
Meanwhile, Iraqi forces announced two neighborhoods in Tal Afar had been freed from the militant group.
IS has also used civilians as human shields to slow the advance of the army.
Early in the morning, iraqi forces were grouped at the gates of the city before entering since several fronts in the city where, according to local officials, a thousand jihadists are cut off.
"It appears more fractured, less robust, and sort of flimsy, is the word I would use", Croft said. "It just seems less coordinated". Islamic State leaders fled Mosul during the fighting there and the whereabouts of its chief, Abu Bakr al-Baghdadi, are unknown. In addition, he said, Iraqi and Jordanian officials are discussing the reopening of the Turaibil border crossing, a almost $1 billion-a-month commerce route.
Brett McGurk, the White House envoy to the anti-ISIL coalition, told the Associated Press news agency that a referendum at this time "would be potentially catastrophic to the counter-ISIS campaign".
Having enabled Iraqi government forces to reclaim the Islamic State's stronghold of Mosul in July, the USA military effort has shown tangible progress and the Pentagon can assert that momentum is on Iraq's side.
Iraqi forces recaptured the first three districts of the Daesh stronghold on the third day of a US-backed offensive amidst an exodus of civilians from the city..
"As we get into the urban areas as we saw in Mosul and Raqqa that's where we'll see the pace slow down, that's where (IS) have placed their defenses", he said.
Daesh fighters inside Tal Afar, estimated to number around 1,000, responded with artillery fire Tuesday as Iraqi forces massed outside the city.
Russia-supported Syrian troops have nearly entirely encircled IS in Syria's central desert region, and the jihadists are also facing twin assaults from the Lebanese army and Shiite movement Hezbollah on the Lebanon-Syrian border. After that, they are expected to focus on pushing IS out of an area dubbed the Middle Euphrates River Valley, stretching north and west from the Iraqi city of al-Qaim into eastern Syria.
A United States official also said Mattis would press Massoud Barzani, president of the autonomous Kurdistan Regional Government, to call off a planned referendum on independence.
"Right now we can expect about 15 brigades - totalling about 15,000 to 22,000 troops - to take part, which is sufficient to crack Tall Afar by December", he said. The Pentagon signed an agreement with Peshmerga forces previous year to provide hundreds of millions of dollars in weapons and equipment.
The United States and other Western nations fear the vote could ignite a new conflict with Baghdad and possibly neighboring countries, diverting attention from the ongoing war against Islamic State militants in Iraq and Syria.