Iraqi government forces are in the third day of an assault on the city of Tal Afar in the country's north-west.
On Tuesday, army and counter-terrorism units broke into Tal Afar from the east and south.
Also, the Syrian Observatory of Human Rights said dozens of civilians have died in two days of intense USA -led strikes on Syria's IS stronghold of Raqqa, as fighting to retake the Syrian city from jihadists nears its densely populated centre.
Mahecic warns that Iraqi civilians inside Tal Afar are likely to be held as human shields by IS militants and those who attempt to flee could be shot.
Iraqi pro-government fighters from the Popular Mobilization Units (Hashd al-Shaabi) launch a rocket towards Daesh Takfiri militants on the outskirts of Tal Afar, Iraq, on August 22, 2017.
In his weekly press conference, Iraqi Prime Minister Haider al-Abadi described Tuesday's progress as "excellent", calling it an "indication of the enemy's collapse". "They have been shown to be unable to stand up to our team in combat".
"It appears more fractured, less robust, and sort of flimsy, is the word I would use", Croft said.
"Today the security for the Iraqi people has been greatly improved", Mattis said, pointing out that Iraqi cities have been liberated, people freed from the terrorists' brutal rule, and the Iraqi economy is recovering.
Iraqi forces had "fought like the dickens in Mosul, (it) cost them over 6,000 wounded, somewhere over 1,200 killed", he said.
A USA official also said Mattis would press Massoud Barzani, president of the autonomous Kurdistan Regional Government, to call off a planned referendum on independence.
The "liberation" of Mosul has restored confidence in the iraqi leadership, has assured Mr. Mattis, even if the iraqi forces were concerned, according to him, "more than 1200 dead and 6000 wounded".
But Mattis declined to make any predictions on the battle. Federal Police together with the Rapid Response Force and the Hashd al-Shaabi are closing in on Mullah Jasim village, considered the largest in the area.
"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.
Citing intelligence, Rasool estimated the number of IS militants inside the town at around 2,000 fighters.
Yet that comeback helped restore the confidence of the Iraqi forces after their shock loss of Mosul and swathes of northern Iraq to IS in 2014, he added.